This is a digital copy of a book that was preserved for generations on library shelves before it was carefully scanned by Google as part of a project to make the world's books discoverable online. It has survived long enough for the copyright to expire and the book to enter the public domain. A public domain book is one that was never subject to copyright or whose legal copyright term has expired. Whether a book is in the public domain may vary country to country. Public domain books are our gateways to the past, representing a wealth of history, culture and knowledge that's often difficult to discover. Marks, notations and other marginalia present in the original volume will appear in this file - a reminder of this book's long journey from the publisher to a library and finally to you. Usage guidelines Google is proud to partner with libraries to digitize public domain materials and make them widely accessible. Public domain books belong to the public and we are merely their custodians. Nevertheless, this work is expensive, so in order to keep providing this resource, we have taken steps to prevent abuse by commercial parties, including placing technical restrictions on automated querying. We also ask that you: + Make non-commercial use of the files We designed Google Book Search for use by individuals, and we request that you use these files for personal, non-commercial purposes. + Refrain from automated querying Do not send automated queries of any sort to Google's system: If you are conducting research on machine translation, optical character recognition or other areas where access to a large amount of text is helpful, please contact us. We encourage the use of public domain materials for these purposes and may be able to help. + Maintain attribution The Google "watermark" you see on each file is essential for informing people about this project and helping them find additional materials through Google Book Search. Please do not remove it. + Keep it legal Whatever your use, remember that you are responsible for ensuring that what you are doing is legal. Do not assume that just because we believe a book is in the public domain for users in the United States, that the work is also in the public domain for users in other countries. Whether a book is still in copyright varies from country to country, and we can't offer guidance on whether any specific use of any specific book is allowed. Please do not assume that a book's appearance in Google Book Search means it can be used in any manner anywhere in the world. Copyright infringement liability can be quite severe. About Google Book Search Google's mission is to organize the world's information and to make it universally accessible and useful. Google Book Search helps readers discover the world's books while helping authors and publishers reach new audiences. You can search through the full text of this book on the web at |http : //books . google . com/ 'eng ' ^^^H m 319 ^^H w/f .07 Mi P# 3Q w SAAf£:s M^ ^^,4.' on. >x HARVARts' UNIVERSITY; vith an appropriation maSe by the Corporatbo for books.ln Engineering. j^€iv^d CLkUv ^S'^ ' y P %^ l^n<l.^H^Of' ^ A- POCKET-BOOK OF MECHANICAL ENGINEERING TABLES, DATA, FOEMULAS, THEOEY AND EXAMPLES FOB ENQINEEB8 AND STUDENTS CHARLES M. SAMES, B.So. MechcMical Engineir SECOND EDITION, REVISED AND ENLARGED SECOND THOUSAND JERSEY CITY, N. J. CHARLES M. SAMES 1907 r / :oU<^'[irK' C^2 -^ » Copyright, 1005. 1006 CHABLBS M. SAHES BOBBBT DBUMMOND, PHIHTBR, NEW TOBK ^ PREFACE. Thib book is the result of the writer's endeavor to compact the greater part of the reference information usually required by mechanical engi- neers and students into a volume whose dimensions permit of its being carried in the pocket without inconvenience. In its preparation he has consulted standard treatises and reference books, the transactions of engineering societies, and his own memoranda, which extend back over a period of fifteen years. A large amount of val- uable and timely matter has been obtained from the columns of technical periodicals and also from the catalogues which manufacturers have cour- teously placed at his disposition. While very great care has been taken in the preparation of manuscript and in the reading of propfs, it is nevertheless a regrettable fact that first editions are not always infallible, and the writer will accordingly be under obligations to those who will call his attention to such errors in statement or typography as may come to their notice. Suggestions indicating how subsequent editions may be made of greater usefqlness are respectfully solicited. Chabuss M. Sambs. SECOND EDITION, FOR 1907. All matter contained in the first edition has been carefully scrutinized for errors, comparisons having been made with the original sources of the infonnation from which it was compiled, as it was found that nearly all the inaccuracies occurred through recopying from notes. A number of alterations have been made in the text, certain data have been replaced by fresher matter, and the work has been enlarged by the addition of an appendix in which new subjects are treated, some omis- sions supplied, and much space given to recent and valuable matter relat- ing particularly to Machine Design. C. M. S. iii CONTENTS. PAGE MATHEMATICS 1 Weights and Measures. Arithmetic. Algebra. Logarithms. Mensuration. Trigonometry. CHEMICAL DATA 10 MATERIALS 11 Properties and Tables of Weights of Metals, Woods, Stones and Building Materials. Weights and Dimensions of Rods, Bars, Pipes, Boiler Tubes, Bolts, Nuts, Rivets, Nails, Screws, Wire-Rope, Chains, etc. THE STRENGTH OF MATERIALS, STRUCTURES, AND MACHINE PARTS 18 Stresses. Strength of Materials. Factors of Safety. Strength of Chains, Ropes, Cylinders, Boilers, Bolts, Fly-wheels, Riveted Joints, Cotter Joints, Shafting, Keys, Springs, Beams, Flat Plates, Stayed Surfaces, Crane Hooks, Columns and Struts, etc. Car- negie Steel Tables. Reinforced Concrete. Graphic Statics. Stress Diagrams for Framed Structures, etc. ENERGY AND THE TRANSMISSION OF POWER 43 Force. Mass. Energy. Power. Elements of Machines. Ma- chine Parts. Connecting-Rods. Shafting. Journals. Ball and Roller-Bearings. Gearing. Belting. Pulleys. Rope Transmis- sion. Friction. Lubrication. Power Measurement, etc HEAT AND THE STEAM ENGINE 66 Heat. Steam. Thermal Efficiencies. Indicator Diagrams. Engine Design and Data. Temperature-Entropy Diagrams. Steam Turbines. Locomotives. Steam Boilers and Accessory Apparatus. Internal-Combustion Engines. Air. Compressed Air. Fans and Blowers. Heating and Ventilation. Mechanical Refrigeration, etc. HYDRAULICS AND HYDRAULIC MACHINERY 106 Hydraulics. Water Wheels. Turbines. Pumps. Plunger Pumps and Pumping Machinery. HydrauUo Power-Transmis- sion, etc. V VI CONTENTS. PAOB SHOP DATA 117 Cupola Data. Welding. Tempering. Screw Threads. Wire and Sheet-Metal Gauges. Fits. Grinding Wheels and Data. Cutting Speeds. High-Speed Tool Steel. Power Required by Machinery. Cost of Power and Power Plants, etc. ELECTROTECHNICS 130 Electric Currents. Electro-Magnetism. Electro-Magnets. Con- tinuous-Current Djoiamos and Motors. Alternating Currents. Alternating-Current Generators. Transformers. Electric Power Transmission. Electric Lighting. Electric Traction, etc. APPENDIX -..^.... 162 SYMBOLS AND ABBREVIATIONS. A Area in square feet. Am. Mach. American Machinist. a Area in square inches. Bm Bending moment. B.H.P. Brake horse-power. B. T. Board of Trade. B.T.U. British thermal unit. B.W.G. Birmingham wire gauge. C. Centigrade. C Modulus of transverse elasticity. C. I. Cast iron. 0. Center. cm. Centimeters. 0; g. ^ Center of gravity. cir. mils Circular nuls. c.-p. Candle-power. cu. Cubic. ^ coe£F. Coefficient. D Larger, or outside, diameter in Inches. d IHameter in inches (diam.). degs. Degrees. B Modulus of direct elasticity. E.H.P. Electrical horse-power. E.M.F. Electro-motive force. E. N. Engineering News. E. R. Engineering Record. E. W. & £. Electrical World and Engineer. F. Fahrenheit. Fn Tractive force in pounds. / Acceleration in feet per second. ^ fet /«. ft ^ Stresses in pounds per square inch (compresnon, shear, ten- sion). fr Modulus of rupture, ft. Feet. ft.-lb8. Foot-pounds. O Pounds in one cubic foot of water. Acceleration of gravity in feet per second ( -^ 32.16) ; Grams, gal. Gallons. S-cal. Gram-calories, r Height or head in feet; total heat in steam above 32<* F.. in B.T.U. H.P. Rated horse-power. h Height in inches; sensible heat in the liquid above 32* F. hor. Honsontal. hr. Hours. / Moment of inertia. Ip Polar moment of inertia. I.H.P. Indicated horse-power. Ing. Taschenbuch. Engineer's Pocket Book (Htltte), Berlin, in. Inches. vii Vm SYMBOLS AND ABBREVIATIONS. K Modulus of volumetric elasticity. ho Specific heat at constant volume. kp " •• «• «• pressure. kg. Kilograms; kg.-m., kilogram-meters. km. Kilometers. kw. Kilowatts. L Length in feet ; latent heat in B.T.U. per lb. of steam. 1 Length in inches, lb. Pounds. lin. Linear. M Poisson's ratio. , M.E.P. See pm. M.M.F. Magneto-motive force, m Mass in pounds— ti;-i-(^. m. Meters, mm. Millimeters, m.-kg. Meter-kilograms. N Number of revolutions per minute. n «• I* «« 4. g^o^jjd. P Total pressure in pounds. p I^ssure, in pounds per square inch. ]/' Pitch, in inches (rivets, screws, gear- teeth), pm Mean effective pressure in pounds per square mch. perp. Perpendicular. Q Flow of air or water in cubic feet per minute. Q *' •••*•• «• •« «• •• •• eecond. R Radius in feet; thermodynamic constant, r Radius in inches; radius of gyration in inches; ratio of ex- pansion, r.p.m. Revolutions per minute. 8 Modulus of section in bending. St " «••«•« torsion. « Side of square in inches ; distance in feet in velocity formulas, sec. Seconds, sp. gr. Specific gravity, sq. Square. T Absolute temperature in degs. F. (also r). Tm Twisting moment. Tn Greater tension in belt or rope. t Thickness in inches ; time in seconds. <• (or t) Temperature, or rise of temperature in degs. F. tn Lesser tension in belt or rope. V Velocity in feet per minute ; volume in cubic feet. t» Velocity in feet per second, vert. Vertical, W. I. Wrought iron. w Weight or load in pounds (also wt.). d. Yards. V. D. I. Zeitschrift des Vereines deutscher Ingenieure. Berlin, a (Alpha) Coefficient of linear expansion in degs. F. ; an angle. (Beta) An angle, r (Gamma) Pitch ansle in si^iral gears. J (Delta) Total denection in feet ; i///= same in inches. 9 " ^Cf di, Ss, dt Deflection or strain per inch of length (due to com* pression, laterally, shear, and tension, respectively), ij (Eta) Efficiencv. 9 (Theta) Angle of torsion. fL (Mu) Coefficient of friction; tangent of friction angle, jr (Pi) Ratio of circumference to diameter — 3. 14159 -{- . p (Rho) Radius of curs^ature in bending. 2 (Sigma) Symbol indicating summation. T (Tau) Absolute temperature in degs. F. ; normal pitch in spiral gears. 4> (Phi) Entropy. oc "Varies as." > Greater than. < Less than. > Parallel to. Across. t MATHEMATICS. WEIGHTS AND MEASUBES (ENGLISH). Length* 1,000 mils"! inch; 12 inches "■I foot; 3 feet — 1 yard: 5.5 yards =-1 rod, pole or perch; 7.92 inches »1 link; 100 links — 1 chain; 80 chains — 1 nme = 5,280 feet ; 1 furlong = 40 rods ; 1 knot or nautical mile -6,080.26 feet - i league. Surface. 144 sq. in. => 1 sq. ft. ; 9 sq. ft. — 1 sq. yd. ; 30.25 sq. yd. — 1 sq. rod; 160 sq. rods-1 acre -43,560 sq. ft.; 1 circ. mil = 0.0000007854 sq. in. Volume. 1,728 cu. in. — 1 cu. ft. ; 27 cu. ft. — 1 cu. yd. ; 1 cord of wood — 128 cu. ft. ; 1 per ch of masonry — 24.75 cu. ft. Avoirdupois Weiglit. (The grain is the same in all systems.) 27.34375 grains — 1 drachm — tV ounce ; 1 pound — 16 oa. — 7,000 grains ; 1 long ton — 2,240 lb. ; 1 net or short ton - 2,000 lb. Troj^ Weiflflit. 24 grains — 1 pennyweight; 20 ^nny weights — 1 ounce; 12 ounces — lib. — 5,760 grains; 1 carat — 3.168 grains ( — 0.205 gram). Apothecaries' Weight. 20 grains — 1 scruple; 3 scruples- 1 drachm; 8 drachms — 1 oz. ; 12 oz. — 1 lb. — 5,760 grains. Liquid Measure. 4 nils — 1 pint; 2 pints — 1 quart; 4 quarts — 1 gal- lon (U. S. gal. -231 cu. m.; British Imperial gal. -277.274 cu. in ); S1.5 gal. — 1 barrel; 2 barrels — 1 hogshead. Apothecaries* Fluid Measure. 60 minims — 1 fluid drachm; 8 drachms — 1 fluid oimce- 437.5 grains. Dry Measure. U. S. 2 pints — 1 quart; 8 quarts — 1 peck; 4 pecks — 1 bushel -2,150.42 cu. m.-1.2445cu. ft. (1 British bushel -8 Imperial gal. - 2,218.192 cu. in = 1.2837 cu. ft.). Circular Measure. 60 seconds— 1 minute; 60 minutes— 1 degree; 90 degrees — 1 quadrant — i circumference Board Measure (B. M. ). No. of feet board measure — length in feet X width in feet X thickness in inches. METRIC MEASUBES. The following prefixes are employed for subdivisions and multiples: MiUi- 0.001, Centi-0.01, Deci-0.1. Deca-10, Hecto-100, Kilo -1,000, Myria- 10,000. Length. 1 meter - 39.3701 13 in. - 3.28084 ft. 1 kilometer - 3,280.843 ft. - 0.62137 mile. 1 inch - 2.54 centimeters (cm. ) - 25.4 millimeters. 1 foot — 0.8048 meter - 30.48 cm. 1 mile — 1.6093 kilometers — 1609.3 meters. Surface. 1 square cm. — 100 sq. mm. —0.155 sq. in. 1 sq. meter (m.) — 10.764 sq. ft. 1 are — 100 sq. m. 1 hectare -100 ares— 10,000 sq. m.— 2.4711 acres. 1 acre — 0.4047 hectare. 1 sq. mile — 259 hectares. 1 sq. ft. -0.092903 sq. m. 1 sq. in. = 6.4516 sq. cm. Volume. 1 stere— 1 kiloliter = l cu. meter — 35.3148 cu. ft. 1 liter (1.) -1 cu. decimeter -61.024 cu. in. = 0.2642 gal. (U. S.). 1 gal. (U. 8.)- 3.7854 liters. 1 cu. cm. = 0.061 cu. in. Weight. 1 gram (or gramme) — 15.432 grains. 1 kilogram (kg.) — 2.20462 lb. avoirdupois. 1 metric ton — 1,000 kg. -2,204.62 lb. 1 griun- 0.0648 gram. 1 lb. = 0.4536 kg. Pressure and Weight. 1 lb. per sq. in. — 0.070308 kg. per sq. cm. 1 kg. per sq. cm. — 14.223 lb. per sq. in. = 1 metric atmosphere. 1 atmos- phere (14.7 lb. per sq. in.) = 2,116.3 lb. per sq. ft. -33.947 ft. of water- 30 in. of mercury (762 mm.) at 62° F. 1 lb. per sq. in. -27.71 in. of water -2.0416 in. of mercury at 62° F. MATHEMATICS, ABITHMETIC AND ALGEBRA. Squares and Cubes of Numbers* Circumferences and Areas of Circles. n n2 n3 ten Kn2-j-4 1 1 1 3.142 0.7854 2 4 8 6.283 3.1416 3 9 27 9.425 7.0686 4 16 64 12.566 12.5664 5 25 125 15.708 19.6350 6 36 216 18.850 28.2743 7 49 343 21.991 38.4846 8 64 512 25.133 60.2655 9 81 729 28.274 63.6173 10 100 1000 31.416 78.6398 11 121 1331 34.558 95.0332 12 144 1728 37.699 113.097 13 169 2197 40.841 132.732 14 196 2744 43.982 153.938 15 225 3375 47.124 176.716 16 256 4096 50.265 201.062 17 289 4913 53.407 226.980 18 324 5832 56.549 254.469 19 361 6859 59.690 283.629 20 400 8000 62.832 314.169 346.361 21 441 9261 65.973 22 484 10648 69.115 380.133 23 529 12167 72.257 415.476 24 576 13824 75.398 452.389 ^5 625 15625 78.540 490.874 26 676 17576 81.681 630.929 27 729 19683 84.823 572.555 28 784 21952 87.965 615.752 29 841 24389 91.106 V 660.520 30 900 27000 94.248 706.858 31 961 29791 97.389 754.768 32 1024 32768 100.531 804.248 33 1089 35937 103.673 856.299 34 1156 39304 106.814 907.920 35 1225 42875 109.956 962.113 36 1296 46656 113.097 1017.88 37 1369 50653 116.239 1075.21 38 1444 54872 119.381 1134.11 39 1521 59319 122.522 1194.59 40 1600 64000 125.66 1256.64 41 1681 68921 128.81 1320.25 42 1764 74088 131.95 1385.44 43 1849 79507 135.09 1452.20 44 1936 85184 138.23 1520.63 45 2025 91125 141.37 1590.43 46 2116 97336 144.51 1661.90 47 2209 103823 147.65 1734.94 48 2304 110592 150.80 1809.56 49 2401 117649 153.94 1885.74 50 2500 125000 157.08 1963,50 51 2601 132651 160.22 2042.82 52 2704 140608 163.36 2123.72 53 2809 148877 166.50 2206.18 54 2916 157464 169.65 2290.22 55 3025 166375 172.79 2375.83 56 3136 175616 175.93 2463.01 57 3249 185193 179.07 2551.76 58 3364 195112 182.21 2642.08 ARITHMETIC AND ALGEBRA. Squares and Cubes of Numbers. Circumferences and Areas of Circles. n n2 ns im «n2-i-4 59 . 3481 205379 185.35 2733.97 60 3600 216000 188.50 2827.43 61 3721 226981 191.64 2922.47 62 3844 238328 194.78 3019.07 63 3969 . 250047 197.92 3117.25 64 4096 262144 201.06 3216.99 65 4225 274625 204.20 3318.31 66 4356 287496 207.35 3421.19 67 4489 300763 210.49 3525.65 68 4624 314432 213.63 3631.68 69 4761 328509 216.77 3739.28 70 4900 343000 219.91 3848.45 71 5041 357911 223.05 3959.19 72 5184 373248 226.19 4071.50 73 5329 389017 229.34 4185.39 74 5476 405224 232.48 4300.84 75 5625 421875 235.62 4417.86 76 . 5776 438976 238.76 4536.46 77 5929 456533 241.90 4656.63 78 6084 474552 245.04 4778.36 79 6241 493039 248.19 4901.67 80 6400 512000 251.33 6026.55 81 6561 531441 254.47 5163.00 82 6724 551368 257.61 5281.02 83 6889 571787 260.75 5410.61 84 7056 592704 263.89 5641.77 85 7225 614125 267.04 6674.60 86 7396 636066 270.18 5808.80 87 7569 658503 273.32 5944.68 88 7744 681472 276.46 6082.12 89 7921 704969 279.60 6221.14 90 8100 729000 282.74 6361.73 91 8281 753571 285.88 6503.88 92 8464 778688 289.03 6647.61 93 8649 804357 292.17 6792.91 94 8836 830584 295.31 6939.78 95 9025 857375 298.45 7088.22 96 9216 884736 301.59 7238.23 97 9409 912673 304.73 7389.81 98 9604 941192 307.88 7542.96 99 9801 970299 311.02 7697.69 100 10000 1000000 314.16 7853.98 Square and Cube Boot by Approximation. From above table take n whose cube or square is nearest tlie number of which the root is desired. For square root, divide the number by n, obtaining the quotient ni; take (n+ni)-*-2 ( = n2) for a new divisor, obtaining ng as a guotient; take (n2+n8)-*-2 for a new divisor and continue process until divisor and quo- tient are alike, or to the reqiured accuracy. For cube root, divide the number by n^, obtaining quotient tii; take ( — r — -J =-n2* for a new divisor, obtaining quotient na; take^ — ^ — '^J for a new divisor and continue process until (2naj + na4.i) + 3 = quotient. Compound Interest. a = c(H-p)*», where a = amount, c— initial capi- tal, p==rate per cent in hundredths, and n = number of years. Binomial Theorem. (a ± 6)» = a» ± na»-i6 + ^-ih^rt(^^^2b2^ n(n-l)(n-2) ^,_, 1.2.3 »6»+ 4 MATHEMATICS. Arithmetical and Geometrical Prosression. Let a » first term of the series, 6 = last term, d = difference between any two adjacent terms (in Arith. Prog.), n = number of terms, » = sum of all the terms, r = ratio of any term divided by preceding one (in Geom. Prog.). Then, for Arithmetical series, b=Q + (n—l)d= a; n « = f{2a + (n-l)d]=.^ + ^'=(6+a)-|=|[26-(n-l)d]. ■El ^ ^ . 1 • 1. - 1 a+(r-l)« (r-l)»r"-l For Geometncal senes , b =» ar^~^ -= — — -^^ — - — ; ; r r" — 1 n—l II— 1 y-^ o(r"-l) ^ r&--a _ 6(r"-l) ^ y^"" y ^" , ^^ log b-logg. Sinlcing Fund for Depreciation and Renewal, a = a(r^ — 1 ) -*■ (r — 1 ), where < is the fund or amount to be accumulated in n years, and r~l plus the rate per cent of interest to be compounded annually, the rate being expressed in hundredths. Example. A certain machine costing $1,000 (a) will need to be replaced by a new one costing the same amount at the end of 10 years (n). What sum must be paid into a sinking fund at the end of each year to amount to $1,000 at the end of the tenth year, interest being compoimded at the rate of 5 per cent ? 1 ,000 = o( 1 .05^° — 1 ) -*■ ( 1 .05 — 1 ; , and a, or the annual amount to be placed in the fund, =$79.50. Interpolation. Where a value intermediate to two values in a table is desired, the following formula may be employed. Value desired. Let N, Nu ^2 and N^ be four numbers (equally spaced) whose tabular functions are a, ai, 02 and 03. Then, in above formula to find Ux, the tabu- jy — jV" lar function of Nx (lying between N and iVi), n = ~ — jv Ni — N 6 = the first of the first order of differences, c= " " " " second ** " " d= " '* " " third " " " , etc. Example. The chords of 30°, 32°, 34° and 36° are 0.5176, 0.5513. 0.5847 and 0.6180, respectively. Find the chord of 31°. a ai 02 aa 0.5176 0.5513 0.5847 0.6180 6= 0.0337 0.0337 0.0334 0.0333 c= -0.0003 -0.0003 -0.0001 d- 0.0002 0.0002 n = (31 - 30) ^ (32 - 30) = 0.5 a.. 0.5176 + OJ>(0.0337) + 0-5( -05)( -00003) +0.5 (-0.5)(- 1.5)(0.0002) J o -0.5345. Logarltlims (log). The hyperbolic or Napierian log of any number equals the common log X 2.3025851. The common log of any number equals the hyperboUc log (loge) X 0.4342945. Every log consists of a whole part (the characteristic) and a decimal part (the mantissa). The mantissa or decimal part only is given in the table?. The characteristic of the log of a number is one less than the number of figures to the left of the decimal point in the number. Log 3 = .47712, log 30 = 1.47712, log 300 = 2.47712, etc Log 0.3= -1.47712, log 0.03= -2.47712, log 0.003= -3.47712, etc. Any logarithm with a negative characteristic as — 1.47712, may be written as 9.47712 - 10. (The sum of 9 and - 10 being - 1.) Formulas for Using Logarithms, log a&=log a+log b. log -^— log a— log 6. logaft = 61oga. logy^a = — ^. TABLE OP CHORDS. JSzamples. 6X4 (using logp); Log 6-* .6 Log 4- .60206 Sum « 1.30103, which is the log of 20, or the result i quired. Midtiply 0.5 by 0.04. log 0.6 =-1.69897- 9.69897-10 log 0.04 2.60206 - 8.60206 - 10 Their sum = 18.30103 - 20 - - 2.30103, or the log of 0.02 For 0.5-«-0.04, diff. of logs» 1.09691- 0-log of 12.5. Rnd nth root of 0.09. log 0.09= -2.95424=8.95424-10 divided by n (say 2) =4.47712-6- -1.47712, or log of 0.8. Kaise 0.3 to nth power. log 0.3= -1.47712 = 9.47712- 10 multiplying by n (say 2) = 18.95424-20= -2.95424 -log 0.09. Log jr-.49715, log ^^ - - 1.50285, log ««-.9943, log'V^.248576. «-3.1416926536+. TABLE OF CHOBDS. Deg. caid. Deg. Chd. Deg. Chd. Deg. Chd. Deg. Chd. 2 .0349 20 .3473 38 .6511 56 .9389 74 1.2036 4 .0698 22 .3816 40 .6840 58 .9700 76 1.2313 6 .1047 24 .4158 42 .7167 60 1.0000 78 1.2586 8 .1395 26 .4499 44 .7492 62 1.0301 80 1.2856 10 .1743 28 .4838 46 .7815 64 1.0598 82 1.3121 12 .2090 30 .5176 48 .8135 66 1.0893 84 1.3383 14 .2437 32 .5513 50 .8452 68 1.1184 86 1.3640 16 .2783 34 .5847 52 .8767 70 1.1471 88 1.3893 18 .3129 36 .6180 54 .9080 72 1.1756 90 1.4142 MENSUBATIOX. AREAS OF PLANE FIGURES (A). Trianglesw pendicular let fall from vertex of opposite angle. Take as base any side which will be intersected by a per- 5, len " Lcm gth of base—d, leng th of ride to the left — a, side to right — c. Then A — y i/ a* — (2 — ~ ^ \ — hh+2, where A = length of perpendicular. Trapezoid. If a, b and /i=lengths of parallel rides and perpendicular, respectiv^y, A =0.5Ma + 6). Circle, (r = radius , d = diameter) A = jtr* = xd^ + 4. Circumf . = nd. Sector of Circle. A = 0.5r X length of arc = 0.008727r2 X degrees m arc. Segment of Circle. A = 0.5[6r — dr — h)]. 6 = arc, c = base, h = height at center of base. Ellipse. Equation referred to axes through center: a V+ 6**2=0*6*, where a —semi-minor axis, & = semi-major axis and x and y are the abscissa and ordinate of any point on the perimeter. A = jtab. L^gth of perimeter \-bJ ^64Va + 6^ 256Va-l-6/ J Parabola. Equation, origin at vertex : y^ = 2px, where 2p is the parame- ter, or double ordmate through focus. Area of any portion from vertex — 2xv 3' MATHEMATICS. Hyperbola. Equation: oV— Wx^— — 0*6*. Cycloid. Lengtn of curve « 4 times diam. of generating circle. Area -=3 " area " " ** Area of Any Irregular Figure. Simpson's Bule. Divide the length of the figure into an even number of equal parts and erect ordinates tlirousli the points of division to touch the boundary lines. Then A = ( ^ j d, where a — sum of first and last ordinates, b — sum of even ordinates, e-"suxn of odd ordinates (excepting first and last) and ^» common distance between ordinates. The greater the number of divisions the greater will be the accuracy. IX>6ABITHMS OF NUMBERS. 00000 0413ti 070 IS 11394 14013 17609 20412 23045 25527 1 00432 04533 08270 11727: 14922 178^ 20683 23300 3576,^ 27876 28103 30103 30320 32222 34242 30173 38021 307 &4 32^28 34439 30361 38202 39907 4149714 14?01 43 136! 43:297 4471644871 40240^ 4t^389 47712 47Bo7 49136149270 505 15' 50051 51S51»51983 53 1 48; 53275 54407. 54531 55t330 55751 J 0820 56937 :i7978, 58093 59106|592IS 60206^60314 61 278! 62325 1^347 64345 65331 6tt276 67210 08124 69030, 69897 70757 716O0 72428 73239 01334 62428 03448 64444 05418 66370 673J3 68215 69108 09984 J„ 00860 04922 08030 13057 15229 18184 20952 23553 20007 28330 30536; 33634 34635 30549 38382 40140 41S,'ia 434r>7 45t>25 46538 4800 1 49415 50786 52114 53403 54654 55871 57054 58200 59329 00423 61490 02531 63548 04542 65514 66404 07394 68305 09197 70070 01284 05308 08991 12385 15634 IBim 21219 ^^805 20245 28556 30750 32838 348,-50 36736 38561 40312 41096 43616 45179 46687 48144 49554 5091Q 52244 53539 54777 5^991 57171 58320 59439 60531 01595 02034 63049 70842 70927 71684 71767 72509 72rj91 73320 7341XJ I I 66010 06558 67486 68395 09285 70157 71012 71850 72073 734841 01703 05690 0034:^ 127 UK ■158,36f 18752[ 21484! 24ftl5 20482 2S780 30903 33041 35025 30922 38739, 40483 4210a; 43775 453;j2 40^35 1 48287 49603 510551 52375 53056 54900 50110 57287 58433 595r>0 0O638 01700 02737 63740 02119 00070 13033 UU37 02531 00446 10037 13354 8 02938 0t»19l 10380 13072, 10435 10732 19033 19312'19590 2174812201122272 24551124797 26951 27184 20226' 2944 7 31387.31597 24304 20717 29003 31I7J 03342 0718S 10721 .1398S 17026 .19866 23531 25042 274 Hi ,29607, 31806 33344 33446;33646 33840 35218' 354 1 1 35003 35793 371071 3 729 1I37475 37658 38917 30094 39270 39445 406.54 40824 40B93 41162 42325! 42488 42(161 42!^ 4: i*>33 , 44091 4 42 48 ' 44 404 454 R 4 4 5 63 7 \ 45788 i 45939 46982 47 1 29 1 47 270 1 47422 48430 4867 3 ' 487 1 4 1 4S856 04040 04738 49831 51189 2504 49969 50106 50243 51322 51455 51587 52034162763152892 53782 53908 54033 54158 55023155145 55267 56388 56239166348 56467 56585 57403157519 57634 57740 58546,58059 58771 '58883 5961H1 59770 59879 59988 60746 60863 00969:01060 03743 07555 1 1059 14301 17319 20140 22789 25285 27646 29K85 32015 34044 35084 37840 39626 41330 429' 44560 46090 47567 48990 50379 61720 53020 54283 55509 56703 57864 58995 (50097 01172 65706 66652 67578 68485 69373 702431 71096' 71933' 72754 7360O 61 805 6 1909 , 6201 4 , 02 1 18 6222 1 02839' 6294 1 03043 6,3 1 44 , 63246 038491 03049 ; 64048 '64147^ 642 J 6 64836 64033 ] 6503 1 ' 65 1 28^ 65225 05801 05890165992 60087. '66 181 66745 06839 60932 67025^ 67117 4^7669' 0776 1 'fi7SrN2 67943 68034 i',sr5 74 (^siiiH r^-.7s:^ *VnH42' 68931 r VJ 4< V ] r ;g rs I Si i >1J ( hU H >97 23 ■ 098 1 fl 7 032y 7 U4 1 5 -05ii i 70686 ' 70672 71181 71265 71349 71433 71517 72016 72099 72181172203 72346 72835 73916 72997.73078 73159 73640 737 19 73799 73878 73957 < I I LOGARITHMS OF NUMBERS. liOGABlXUMS OF NUMBERS (CorUiniMd), 74036 74819 75587 76343 770S5 77315 78533 7&230 7B934 30^18 81291 31Q54 82607 8325 1 S4510 85126 85733 863,12 86923 S750a 88081 88049 $9209 80753 90OO& 30849 91381 91908 92428 92942; 93450 93952 944^8 9493'J 95424 95S04 96379 96848 97313 97772 98227 98677 99123 99564 3 74115 74194 74273 74353 7442U 74896 74974 l75aT I 7512!^ 75205 75(k't4 757>i0 7r>S|-) ZA^IM 75967 76418 76492 7ti5rp7 7ii<v(] 77159 77232 77;jlU. 77887 77060 7S*W2 6 78604 79309 SQ003 80686 81358 82020 82672 8.1315 R394S 84572 85187 85704 86392 86932 87564 88138 SS705 89265 89818 90902 91434 ,91 960 192480 ,92903 93'JOf} 94002 044 9H 94988, 95472, 05952 96426 968951 97359 97818 98272 98722 99167 99607 78675 79379 80072 S0754 81425 82086 S2737 83378 H4011 84^4 S524& 85854 86451 S7940 87*^22 8811>f'. 8871.1' 89321 89873 90417 78749 79449 80140 80821 81491 82151 82802 83442 84073 84696' 85309 8h5914 ,86510 Ift7099 s.sv I V •K9:i7(J ,89027 90472 7*^716 74507 75282 76042 76790 74.^6 358 76118 70864 77379 77452.77525 77597 78104 78 176i 78247 78319 78817 79518 ,90209 80889 81558 82217 82866 83506 S4136 84757 S5370 85974 R6570 'S71S7 *?77,17 >i*H32 89082 90526 90956 91009 91062 914S7|91 540 91593 920]?rj20a' 921] 7 92ri:M 1J:.'"iM '.i2m4 930 r^ u\ii\:i:, ij;i]46 93551 rK^<>< 11,93051 M4052,B4iOi;n4]51 BI 54 7, 04 500 94m .95030 95085 95521 95569 I I 95990 9fK}47 96473 96520 96042 9608« 97405 97451 97864; 97900 9S318 98363 98767 99211 99051 9881 99255 99605 )G134 95017 96095 96567 97035 97497 979^ 9S4D8 98856 99300 09730 78S8S 7958S 80277 80956 81624 82282 82930 83569 84108 ^4819 85431 86034 89629 87216 *<770r, IsMJUU: SS94.S' 9003 90580 91116 91645 92169 92686 9319: 037n2 1M'2i)l 05182 95(m'j 00142 ^66 14 97081 43 0800(J 98453 989m 99344 99782 78958 7965: 80346 81023 816^ 82347 82995 83632 84261 84880 85491 86094 86688 87274 8 9 74663 74741 75435 7551 1 76HIH 7 '1 2',^ 7093S.77i,H 767U 7774^:i 78390 78462 79020 70O09 >7:7 7f'7tKi S(U I A S01S2 XlylWj ts]158 81757 82413 83059 83696 84323 84942 85552 86153 86747 87332 >i7010 80^42 S950' 90091,00146 00a34 90687 91169 91098 92221 92737 93247 93752 94250 94743 95231 95713 01222 91751 02273 92788 9329S 93802 94300 94702 95279 95761 96190 9023? 95t16l 196708 97128 97174 97580.07635 98046 98091 98I98 98h543 9«945 9S989 99:i88 99432 99826190870 81823 8247S 83123 83759 84386 85903 S5612 86213 86806 87390 8706: 88536 89008 89653 9020iJ 00741 70169 71 79865 80550 81224 81889 82543 83187 83822 84448 8506,'> 85673 86273 ^S64 87448 8S024 88593 89154 S07O8 90255 90795 Diff. 91275 91328 01803 92324 92840 93349 93852 94349 9484! 9533S 958D9 91855 92376 92891 93399 93902 04399 94899 95370 DS3S6 06284^96332 96755 96802 97220 97267 97681 197727 08137,98182 98588 99034 99476 99913 99078 99620 90957 Note. — ^The diflferencea in the last column are mean values only. For accurate values the difference between any two consecutive values should be found by subtraction. SUBFACES (A) AND TOLUMES (T) OF SOLIDS. «i3 Sphere. A=43ir*=»«cP. V= -=0.5236d3. Bins of Circular Cross-section. A = 9.8696Z>d. V = 2.4674Dd2. (D = outside diameter— d; d = diam. of cross-section.) 8 MATHEMATICS, Segment of Sphere. A - 2iark » area of base + ir^^ (A >» beightX Cone. A-«»Vr2+A2. F=0.261&i2A (A -vert, height). Conic Frustum. ^ * -|<Z> + <i) X slant height, A. Cylinder. Ellipsoid. Pyramid. F-6.5236Z>d2. Paraboloid, F=»-5-Xarea of base. Iving a3 i. F = 1.5708r%. 3 Frustum of Pyramid. V TBIGONOMETBY. 10 ^ -^A+a+vCla) (A and a -areas of basest. Fis.;i. Functions of the angle BOE{=x). -&fi=»sine, Oj& = cosine, E-A -versed sine, (?C— versed cosine, -4.2)= tangent, (ri'''- cotangent, OD — secant, OF = cosecant. , ^ , v Formulas. (A, J5 and C are angles.) tan A-^4; cotA-^; secA = — -r; cosecA-^— r; cos A sin A cos A sin A sin^ A+cos2 A-1; versin A-1— cos A; covers A — 1- sin A. ««, /* J _i_ R\ SI ain >f Ana /? -I- cna A Hin J?. ; tan A — cot A' Bin" A T COS" .«.==*; voioiii -^ — J- vv»o ^i sin (A ±5) —sin A cosB±cos A sin B. cos (A ± B) —cos A cos BT sin A sin R . ^ ^ . A A Bin A — 2 sin -g ®*^ "J' l-cosA-2sin2 2* A A cos A — cos^ -g — sin^ -^, l+cosA=2cos2:^. tan A tan-^. tan A-2tan|^-^[l-tan2^]. sin A+cos A=sin (^+a)V2: cosA-smA-sm(^^-AjV2. ^^^ ^ = tan (A ±fi) -[tan A ±tan fi]^[lT tan A tan fi], cot (A ±B) -[cot A cot B^ l]-5-[cot A ±cot B]. sin A±sin B— 2sm — 5 — ^'^^ — 2~* „ „ A+B A-B cos A +COS B = 2 cos — g — ^^ ~2 — * D " . A+B . A-B cos A —cos B - —2 sin — ^ — ^° — 2 — * rin A sin B-^ cos (A-B) -^ cos {A+B), cos A cosB — icos (A+B) + ^cos {A — B), sin A cos B = i sin (A+B) + i sin (A-B). sin 3A —3 sin A -4 sin^ A. cos 3 1 =4 cos^ A -3 cos A. 'cos A ±1 sin A)« =cos nA ±i sin nA (i — n/^). NATURAL TRIGONOMETRICAL FUNCTIONS. If A + B+C-180**-K (the three angles of a triangle), then sin ^+8in fi + sin C— 4 cos -g- cos -5- cos •^. ABC cos ^+cos 5+cos C'=l + 4 sin -^ sin -^ sin -5-. tan A +tan B + tan C-^tan A tan B tan C. NATURAL TRIGONOMETRICAL FUNCTIONS. Degs. Sine. Tangent. Degs. Sme. Tangent. .00000 .00000 90 46 .71934 1.03553 44 1 .01745 .01746 89 47 .73135 1 07237 43 2 .03490 .03492 88 48 .74314 1: 11061 42 3 .05234 .05241 87 49 .75471 1.15037 41 4 .06976 .06993 86 50 .76604 1.19175 40 5 .08716 .08749 85 51 .77715 1 . 23490 39 6 .10453 .10510 84 62 .78801 1.27994 38 7 .12187 .12278 83 53 .79864 1.32704 37 8 .13917 .14054 82 •54 .80902 1.37638 36 9 .15643 .15838 81 55 .81915 1. •42815 35 10 .17365 .17633 80 56 .82904 1.48256 34 11 .19081 .19438 79 57 .83867 1.63987 33 12 .20791 .21266 78 58 .84805 1.60033 32 13 .22495 .23087 77 59 .85717 1.66428 31 14 .24192 .24933 76 60 .86603 1.73205 30 16 .25882 .26795 75 61 .87462 1.80405 29 16 .27564 .28675 •74 62 .88295 1.88073 28 17 .29237 .30573 73 63 .89101 1.96261 27 18 .30902 .32492 72 64 .89879 2.05030 26 19 .32557 .34433 71 65 .90631 2.14461 25 20 .34202 .36397 70 66 .91355 2.24604 24 21 .35837 .38386 69 67 .92050 2.36585 23 22 .37461 .40403 68 68 .92718 2.47509 22 23 .39073 .42447 67 69 .93358 2.60509 21 24 .40674 .44523 66 70 .93969 2.74748 20 25 . 42262 46631 65 71 .94552 2.90421 19 26 .43837 .48773 64 72 .96106 3.07768 18 27 .45399 .50952 63 73 .95630 3.27085 17 28 .46947 .53171 62 74 .96126 3.48741 16 29 .48481 .55431 61 75 .96593 3.73205 15 30 .50000 .57735 60 76 .97030 4.01078 14 31 .61504 .60086 59 77 .97437 4.33148 13 32 .62992 .62487 58. 78 .97815 4.70463 12 33 .64464 .64941 57 79 .98163 5.14455 11 34 .66919 .67461 56 80 .98481 5.67128 10 35 .57368 .70021 55 81 .98769 6.31375 9 36 .68779 .72654 54 82 .99027 7.11537 8 37 .60182 .75365 53 83 .99266 8.14435 7 38 .61566 .78129 62 84 .99462 9.51436 6 39 .62932 .80978 61 85 .99619 11.43005 5 40 .64279 .83910 50 86 .99756 14.30067 4 41 .65606 .86929 49 87 .99863 19.08114 8 42 .66913 .90040 48 88 .99939 28.63625 2 43 .68200 .93262 47 89 .99985 57.28996 1 44 .69466 .96669 46 90 1.00000 Infinite 45 .70711 1.00000 45 Cofline. Cotangent. Degs. Cosine. Cotangent. Degs. For intermediate values reduce angles from degrees, minutes and seconds to degrees and decimal part of a degree (e.g., 46° 21' 30" =■46.3583°) and employ interpolation formula. CHEMICAL DATA. Atomic Weights and Symbols of Elements. Aluvninovn. . Al 26.0 Molybdenum . Mo 95.3 Antimony. . Sb 119.3 Neodymium . Ne 142.5 Argon A 39.6 Neon 19.9 Arsenic As 74.4 Nickel . Ni 58.3 Barium. . . . Ba 136.4 Nitrogen . N 13.93 Bismuth. . . . Bi 206.9 Osmium . Os 180.6 Boron B 10.9 Oxygen Palladium . O 15.88 Bromine Br 79.36 . Pd 106.7 Oadmiu'n Cd 111.6 Phosphorus . P 30.77 Ciesium. . . . Cs 132 Platinum . Pt 193.3 Calciimi Ca 39.8 Potassium . K 38.86 Carbon C 11.91 Praseodymium . Pr 139.4 Ceriimi Ce 139 Radium . Ra 223.3 Chlorine. . . . a O Co 35.18 61.7 58.56- Rhodium. . Rh . Rb . Ru 102.2 fJhrnTniiifn. . Rubidium 84.8 Cobalt Ruthenium 100.9 Columbium (Nio- Samarium . Sm 148.0 bium) CJb 93.3 Scandium . 8c 43.8 Erbiimi.*.*.* '. Chi 63.1 Selenium . Se 78.6 E 164.8 Silicon . Si 28.2 Fluorine. . . . F 18.9 Silver . Ag 107.12 Gadolinium. Gd 155 Sodium . n5 22.88 Galliiun. . . . Ga 69.5 Strontium . Sr 86.94 Germanium. CJe 71.9 Sulphur . S 31.83 Glue in urn (Beryl- Gl 9.03 Tantalum . Ta 181.6 lium) Tellurium . Te 126.6 Gold Au 195.7 Terbium . Tb 158.8 Helium He 4 1.00 113.1 Thalium Thorium . Tl . Th . Tm 202.6 Hydrogen. . Indium H In 230.8 Thulium 169.7 I Ir 125.9 191.5 Tin . Sn . Ti 118.1 Iridium Titanium 47.7 Iron Fe 55.5 Tungsten . W 182.6 Krjrpton. . . K 81.2 Uranium. . U 236.7 Lanthaniuh. La 137.9 Vanadium . V 50.8 Lead Pb 205.35 Xenon . X 127 Lithium. . . . Li 6.98 Ytterbium . Yb 171.7 Magnesium. Mg 24.18 Yttrium . Yt 88.3 Manganese. . Mn 54.6 Zinc . Zn 64.9 Mercury. . . . Hg 198.5 Zirconium . Zr 89.9 Calculation of the Percentage Composition of Substances. (1) Add together the atomic weights of the elements to obtain the molec- ular weight of the compound. (2) Multiply the atomic weight of the element to be calculated oy the number of atoms present (as indicated by the subscript number) and by 100, and divide by the molecular weight of the compound. Example. Find the percentage of sulphur in sulphuric acid (HSSO4). Ha + S + O4 (1 X2) -h 31.83 + (15.88X4) =97.35, or the molecular weight. 3183 + 97.35 —32.59, or the percentage of sulphur in the acid. Weights of Gases. Avogadro's law: "In equal volumes of all gases there are the same number of molecules.'' It follows from this law that the weights of equal volumes of all gases are proportional to their molec- ular weights. The molecular or formula weight in grams of any gas occupies 22.4 liters at 0^ C. and 760 mm. pressure. Example. Find the weight of one liter of carbon dioxide ((X)2). Molec- uUr wt. of (X)2-11.91 + (16.88X2)-43.67. .*. 43.67 grams=22.4 Uters. or 1 liter weighs 1.95 grams. (1 cu. ft. = 28.517 fiters; 1 Uter=0.03532 ou. ft.* 1 lb. = 453.5924 grama: 1 gram = 0.0022046 lb.) 10 MATERIALS. Cast Iron (C. I.). Sp. gr.=7.21; wt. per cu. in. -0.261 lb. Fusing point of white iron -1,962* F.j— gray iron, 2,192® F. Chemically com- posed of iron (Fe), carbon (C) (graphitic and combined), silicon (Si), phos- phorus (P), sulphur (8) and manganese (Mn). Contains 3.5 to 4% of totid carbon, the hardness of castings varying directly with the amount of combined carbon. Si (from 0.6 to 3.5%; produces softness and strength proportional to amoimt contained. (Best at 1.8%.) S beyond 0.15% is prejudicial, producing blow-holes and -brittleness when hot. P promotes fluidity but causes brittleness when in excess of 1%. Mn assists the car- bon in combining and confers the property of chilling. It should not ex- ceed 1%. Wrought Iron (W. I.). Sp. gr. =7.78; wt. per cu. in. -0.282 lb. Con- sists of over 99% pure iron +0.3% combined carbon + 0.14% each of 8, Si and P. Steel. Cast steel, sp.gr. -7.92; wt. per cu. in. -0.286 lb. Forged steel, sp. gr.-7 82: wt. per cu. m. -0.283 lb. Fusing point -2500 to 2,700*» F. Temper (or content of carbon). Castings, 0.3 to 0.4%; forgings, 0.25 to 0.3%: chains, 0.15 to 0.18%; laminated springs, 0.4 to 0.6%; boiler plates, 0.17 to 0.2%; same, for welding, 0.15 to 17%; tool steel. 1.7%. Mangranese Steel (containing 14% Mn) has double the strength of ordi- nary steel combined with great hardness. Nickel Steel (3 to 5% Ni) has 30% greater tenacity and 75% greater elastic strength than ordinary mild steel, along with equal ductility. Har- veyised, for ship armor, it offers the same resistance with 43% lees weight. Chrome Steel (0.4% C+1%. of Chromium (Cr) + 2% Ni) is of extreme hardness (self-hardening) and is used for safe walls, projectiles, and cutting tools. Tunffgten Steel (Mushet's) is a self-hardening steel for tools, shells, etc. ^ Mn+2.58% Tungsten (W)). rcu. in. -0.321 lb.* gr. — 6.86 (cast) ; wt. per cu. in. — 0. "• 248 lb. ; fusing point - 787** F. Tin (Sn). Sp. gr- = 7 3 ; wt. per cu. in . 0.264 1b; fusing point -446* F. Aluminum (AD. Sp. gr = 2 66 (cast) and 2.68 (roUed); wt. per cu. in. -0.092 lb. (cast) and 0.097 lb. (rolled). Fuses at 1,213<> F. Mercurr (Hg). Sp. gr. - 13.619 (at 32<» F ) and 13.68 (at 60* F.) ; wt. per cu. in. -0.493 lb. (at 32* F ) and 0.491 lb. (at 60*F.). Fuses at -39* F. Gun Metal Bronze (80 to 90% Oi + 20 to 10% Sn) Strong and tough. Increasing the content of tin increases the hardness Phosphor Bronze (86% Cu+15% Sn+0 6 to 0.75% P) has the toughness of W I. Man- ganese Bronze (81% Cu + 12% Sn + 7% Mn) is even stronger. Silicon Bronze (Chi +3 to 5% Si) has a breaking stress of 66,000 to 75,000 lb. per sq. in., but at and around 6% Si, is brittle. Aluminum Bronze (Chi +5 to 11% Al) has a slightly greater strength. Brass (60 to 70% Chi +40 to 30% 2S1). Babbitt (89.3% Sn + 3.6%x3u+7.1% Sb (antimony)). Alloys. (E. A. Lewis, Eng^eering, 3-31-06.) Cu. Sn. Zn. Pb, P. Si. For steam or gas pressure. ... 87 9 2 2 ** hydraulic pressure 86 12 2 * * bearings. . . : 84 8 8 Phosphor-bronxe 84 14 2 0.06 Copper castings 99.75 0.25 11 12 MATERIALS. Delta Metal (92.4% Cu+2.38% Sn+5.2% Pb (lead)). Mai^olla ]IIetal(83.55% Pb + 16.45% Sn). Tobin Bronie(59% Cu + 2.16% Sn+0.3% Pb+38.4% Zn). Solder. 2 Sn + 1 Pb fuses at 340*» F.. 1 Sq + 2 Pb fuses at 441° F.. and 20 Sn + 1 Pb (for aluminum) at 550** F. Woods. Average Sp. Gr. and Weights per Cu. Ft. Sp. Gr. Wt. Ash 0.72 45 Beech 73 46 Birch 65 41 Cedai- 62 39 Elm 61 38 Sp. Gr. Wt. Fir 0.59 37 ffickory 77 48 Hemlock. . . .38 24 Maple 68 42 White Oak.. .77 48 Sp.Gr. Wt Red Oak. . . 0.74 46 White Pine. .45 28 YeUowPine. .61 38 Poplar 48 30 Spruce 45 28 Stones and Miscellaneous Building Materials. Sp.Gr. Wt. Asbestos 3.07 192 Asphaltum 1 . 39 Bnck (com.). )ressed). (com.] (press( (fire). 1.6 2.16 2.24 1.92 0.96 Oay. Gement, Rosendale Portland 1.25 Earth (loose) 1.28 Granite 2.6 87 100 135 140 120 60 78 80 165 Sp. Gr. Graphite 2.16 2.64-2.93 2.7-3.2 2.5e-2.88 2.8 2.64 (Wts. in lbs. Glai?3, LinioHrcirie Marl >]-■.. . Uin, Rvil>htr 0.933 SahtJ. 1.9 S&[i'J^t«iLic. ... 2.4 Sbto. . 2.88 per cu. ft.) Wt. 135 164r-183 170-200 160-180 173 165 58.4 122 150 180 Weight of Bods, Bars, Plates, Tubes, and Spheres of Metals. Square Flat Round Plates, Bars, Bars, Rods, Spheres, Material. ^„f*. lbs. per lbs. per lbs. per lbs. per lbs. lin. ft. lin. ft. lin. ft. sq. ft. Lbs. per cu. ft. Cast Iron 450 Wrought Ircm. . 480 Steel 489.6 Copper 552 Brass (65 Cu+ 35 Zn) 523.2 Aluminum 166.5 For tubes, multiply numerical coeff. for round rods by (dP—di^). For hollow spheres, multiply numerical coeflf. for spheres by (cP- ««side of square, &=* breadth, t =- thickness, d^extemid diam., di nal diam., all m inches. 1586d» 0504<«« di3). inter* Weight of Square and Bound Wrought Iron Bars In Lbs. per Lineal Foot. d. Rd. Sq. T Rd. Sq. «or d. Rd. Sq. .010 .013 h \ 1.237 1.576 H 6.913 8.802 .041 .052 1.473 1.875 1 8.018 10.21 .092 .117 ^ 1.728 2.201 1 9.204 11.72 .164 .208 2.004 2.552 2 10.47 13.33 .256 .326 1 2.301 2.930 2 13.25 16.88 .368 .469 2.618 3.333 2 16.36 20.83 .501 .638 1 3.313 4.219 2 19.8 25.21 .654 .833 i- 4.091 5.208 3 23.56 30 .828 1.055 !• 4.95 6.302 3* 32.07 40.83 1.023 1.302 1 5.89 7.5 4 41.89 53.33 (»=»si< leo f sq. in in. in in ) Lbs. per sq. ft. = thickness in inches (obtained from gauge tables) X40, ~ "" 43.6 re • ' in in. lbs. lbs. .028 .022 .018 1.12 0.88 0.72 1.41 1.11 0.91 MISCELLANEOUS TABLES AND DATA. 13 IVeisht of Flat W. I. Bars (1 in. wide) in Lbs. per Lineal Foot. Thick- x.^ Thick- x^- Thick- tv ness. ^^' nesB. ^^' ness. ^^' iV .208 ^ 1.46 i 2.50 •r .417 I 1.67 ft 2.71 A .625 A 1.88 1 2.02 I .833 I 2.08 ft 3.13 A 1.04 tt 2.29 1 3.33 i 1 . 25 Thickness in in. For steel add 2%. 'Weiffht of Iron, Steel, Copper and Brass Sheets per Square Foot. Lbs. per sq. ft. = thickness 40.8, 46, or 43.6 respectively. Corrugated and Flat Iron. Lbs. per Sq. Ft. Thickness Flat, Corr., Thickness Flat, Corr., in in. lbs. lbs. .065 2.61 3.28 .049 1.97 2.48 .035 1.4 1.76 If galvanised, add 0.34 lb. per sq. ft. for flat plates and 0.43 lb. for cor- nupated plates. End laps 4 in. mid 6 in. Side laps ™ I corrugation =» 2.5 in. Tin Plates. (Tinned sheet steel.) Usual roofing sizes are 14 X 20 and 20 X 28 (in inches). No. 29 B. W. G. weighs 49.6 lb. per 100 sq. ft. ; No. 27 weighs 62 lbs. per 100 sq. ft. Sooflns Slate. (1 cu. ft. weighs 175 lb.) Thickness in in i A i f ^ ♦ i Lbs. per sq. ft 1.81 2.71 3.62 5.43 7.25 9.06 10.88 Slates are generally laid so that the third slate overlaps the first by 3 in. Sq. in. of roof covered by 1 slate — 0.56(i — 3). No. of slates required for 1 square (100 sq. ft.) » 28,800 -!-&(; -3). (6 and I are breadth and length in in.) Sixes: 6 to 9X12, 7 to 10X14, 8 to 10X16. 9 to 12X8. 10 to 16X20, 12 to 14X22, 12 to 16X24, 14 to 16X26. (Increases by steps of 1 in.) Pine Shingles. No. per 100 sq. ft.-»3,600-«-no. of inches exposed to weather. Wt. in lbs. of 100 sq. ft. = 864-5-no. of inches exj^osed to weather. SlcyUght and Floor Glass. Lbs. per sq. ft. » 13 X thickness in inches. FlasKins. Wt. in lbs. per sq. ft. = 14 X thickness in inches. Approximate Weights of Booflng materials. (Lbs. per 100 sq. ft.) 1 in. sheathiig: spruce, 200; northern yellow pine, 300; southern yellow ?ine, 400; chestnut and maple, 400; ash and oak, 500. Shingles, 200; in. slate, 900; iV in. sheet iron, 300; do.,^th lath, 500; corrugated iron, 100-375; galvanized flat, 100-350: tin, 70-125; felt and asphalt. 100; felt and gravel, 800-1,000; skylights (glass A-i), 250-700: sheet lead, 600-800; copper, 80-125; rinc, 100-200; flat tiles, 1,500-2,000; do., with mortar, 2,000-3,000; pan tiles, 1.000. Weltrht of Cast-iron Pipe per Lineal Foot. Wt. in lbs. - 9Alt(d + 1) , where dTand t are the internal diam. and thickness of metal in in. The wt. of the two flanges »wt. of 1 ft. of pipe. For copper, multiply by 1.226; forW.I.,byl.&7. Welffht of Cast-iron Water and Gas Pipes per Lineal Foot. Siaeinin 4 8 12 16 20 24 30 36 42 48 60 Water, lbs. per ft. 22 42 75 125 200 250 350 475 600 775 1330 Gas, •• •• •* 17 40 70 100 150 184 250 350 383 642 900 Thickness of Cast-iron Water Pipes. <-0.00006(A-l-230)d-h0.333-0.0033rf, where h==head of water in feet, t and d are thickness and diam. in in. Riveted Hydraulic Pipe. (Pelton Water Wheel Co.) Head in feet that pipe will safely stancf=48,600<-5-d. Weight in lbs. per lin. ft.'^cdi. e» 15 for 4 in. pipe 14 up to 8 in. pipe, 13 up to 12 in.. 12.5 up to 24 in. and 12 up to 42 in. pipe* 14 MATERIALS. Wrought-iron Pipe Dimensions and Threads, tf. S. Standard* Internal Diam Internal Diam Nominal in in. Actual in in. |i 1^ l-a 1-^ 5.S li l-a i^ |S §.3 iz; a-a ^^ i .270 .068 .24 27 4^ 4.508 .246 12.49 8 .364 .088 .42 18 6 5.045 .269 14.50 8 .494 .001 .56 18 6 6.065 .28 18.76 8 .623 .109 .84 14 7 7.023 .301 23.27 8 .824 .113 1.12 14 8 7.982 .322 28.18 8 1 1.048 .134 1.67 11.5 9 9.001 .344 33.70 8 U 1.38 it 1.611 .140 2.24 11.5 10 10.019 .366 40 8 .145 2.68 11.5 11 11. .876 46 8 2 2.067 .154 3.61 11.5 12 12. .375 49 8 2i 2.468 .204 5.74 8 13 13.25 .375 64 8 3 3.067 .217 7.54 8 14 14.25 .375 68 8 3^ 3.548 .226 9. 8 15 15.26 .876 62 8 4 4.026 .237 10.66 8 Standard Boiler Tubes. Lap-welded Charcoal Iron. (Morris Tasker &Co.) Outside Inside Lbs. Outside Inside Lbs. diam. in. per ft. diam. in. diam. in. per ft. 1 0.856 0.708 1 3.262 4.272 1.106 0.900 3.512 4.59 1.334 1.25 4 3.741 6.32 1.56 1.666 ^ 4.241 6.01 2 1.804 1.981 6 4.72 7.226 2.064 2.238 6 6.699 9.346 2.283 2.755 7 6.667 12.435 2.533 3.045 8 7.636 16.109 3 2.783 3.333 9 8.616 18.002 i 3.012 3.958 10 9.573 22.19 Surface of tube 1 ft . long in sq.ft .-0.2618Xdiam.inin. Wrought-iron Welded Tubes. Extra Strong. Actual Diameters in in. Nommal diam. in. Outside. Inside. Ex. Inside, Double Strong. Ex. Strong. . , 0.406 0.206 , . 0.54 0.294 . . 0.675 0.421 . . 0.84 0.542 0.244 . ■ 1.05 0.786 0.422 1 1.316 .951 0.687 t 1.66 1.272 0.884 1.9 1.494 1.088 2 2.375 1.933 1.491 i 2.875 2.315 1.765 3 3.5 2.892 2.284 i 4. 3.358 2.716 4 4.5 3.818 3.136 prox. Lead Pipe. Safe working pressure in lbs. per sq. in.^l,000t-t-d. Ap> ox. wt. in lbs. per ft- = 15 5<(caliber+0- t (thickness) and d (diAra.) in in. laSCELLANEOUS TABLES AND DATA. 15 Number of Square and Hexagonal Nuts in 100 lbs. Standard; chamfered, trimmed and punched for standard taps.) Bolt diam. in in. No. Sq. 7270 2350 1120 640 380 No. Hex. 7615 3000 1430 740 450 Bolt diam. in in. 1* No. Sq. 170 130 96 58 No. Hex. 216 148 111 Bolt diam. in in. H 2 No. Sq. 34 23 19 12 9 7.3J (U. S. No. Hex. 40 29 21 15 11 8.5 Bolts. Approximate Weight per Hundred. in lbs.— a +(5 X length in in.). Bolt diam. i f ^ f i I 1 Sq. heads and nuts. a »2 5.7 11 23 39 63.6 97 & »1.4 3 5.6 8.4 12.2 16.6 22 Hex. heads and nuts. a -1.2 3.7 7 16 27 48 64 & »1.4 3 5.6 8.4 12.2 16.6 22 Weight of 100 bolts li li If U 105 30 66 190 35 150 35 230 40 180 40 325 50 260 50 Bridge Biyets. Weight per 100. (5 X length under head in m.). Weight of 100 rivets in lbs.«a+ Diam. in in. f a =1.8 5.8 5.55 Sise. No.. h -3.13 Track Spikes. f 11.1 8.7 13.8 12.5 22.7 17 1 38.8 22.25 If 58.1 28.15 Number in Keg of 200 Lbs. 6XA 650 5Xi 520 5XA 393 Xf 5iXA 384 6XA 350 83.6 34.8 6Xt 260 Wire Nails and Spikes. Numl^er in One Pound. 1550 760 350 190 187 ^^ ^sr" B»^^- ^>^«- 1 1200 1^ • 432 2 252 2i 132 3 87 3i 51 4 35 4^ 27 5 21 5f 15 6 12 6i in., 9; 7 in., 7; 8 in., 5; 9 in., 4^. Ijag Screws. Approximate Weight per Hundred, lag screws in lbs.— a +(&X length in in.;. Diam. in in f ^ i a 2.2 5.7 8 h 2.9 3.3 4.6 Siie. 4d 6d Sd lOd led 20d dOd 40d 50d eod Spikes 876 367 204 43 31 24 18 Finish- ing. 1350 584 310 170 121 72 54 46 Barbed roof. 411 165 103 Spikes. 50 35 26 20 15 12 10 7.2 Weight of 100 10 Iron Wire. Tensile Strength per Square Inch of Section. Diam. in in 0.05 Strength in lbs 106,000 0.1 97,500 0.2 87,500 0.3 81.000 0.4 79.000 The above for bright, charcoal iron wire. If annealed take 75% of values. For Bessemer steel add 10% aqd for crucible steel 15%. 16 MATERIALS. Galvanized Iron Wire. Weight and Resistance per Mile. - bin ^ ?k»J* Lbs. Ohms, gauge. 6 550 10 7 470 12.1 8 385 14.1 (Roe bung.) ?;»^* Lbs. Ohms, gauge. 9 330 16.4 10 268 20 11 216 26 ?;»J' Lbs. Ohms, gauge. 12 170 32.7 13 100 52.8 14 62 91.6 Galyadiized Steel-wire Strand (7 wires twisted). (Roebline.) Diam. of rope, in. ...i A f A i A i Wire gauge No 8 10 11 12 15 17 20 Lbs. per 100 ft 52 36 29 21 10 6 2.4 Estimated breaking strength in lbs.«=160Xwt. in lbs. of 100 ft. Wire Hoisting Bope. (Roebling.) Made from i. to 2f in. diam., 6 strands of 19 wires each, hemp center. Wt. in lbs. per ft. — 1.58<P. Ap- prox. breaking strain in lbs. = ccP. Diam.inin., d= 1.5 1 0.5 Swedish iron, c= 30,000 32,000 35,000 Cast steel, c= 60,000 64,000 70,000 Transniission or Haulage Bope. ih to H in. in diam., 6 strands of 7 wires each, hetaip center. Diam. in in., (2 » 1.5 1 0.5 Swedish iron, c»» 30,000 32,000 33,500 Cast steel, c=60,000 64,000 67.000 Extra Strong Crucible Cast-steel Bope (6 strand, hemp center). Diam. m in., d= 2.5 1.5 1 0.5 19 wire strand, c = 70,000 75,000 78,000 81,000 7 '* •• c- 70,000 75,000 78,000 Crane Chains (Pencoyd). Pitch in in. (c. of 1 link to c. of next), p"=0.17 + 2.43d (where d<li in.); = 2.75d- 0.156 ( *• rf>liin.); d=diam. of link wire in ins. Outside width of link =* 3.3d + t'j in. approx. Approx. wt. per ft. in lbs.: for d = i to ^ in., wt. = 0.876 + 6.5(d — t); for d«itoi in., wt. = 2.5 + 14.6(d-i); ford = |to U. wt. = S + 21.9(d-|). DBG Special Chain. Average breaking strain in lbs. = 62,000^2, when d^ f in., and 62,000d2 - 6,800(d - i) , when d>i in. For proof test take i of these values, and for safe load i. Ordinary crane chains have from 87 to 90% of the strength of the DBG special chains. Chain sheaves should have a diameter of not less than 70d. Holding Power of Nails and Spikes. (Approximate.) Force in lbs. required to withdraw nail = c«^ where i=* length of nail in the wood in in., and <— circumference of a round nail or the four sides of cut nail in in. Values op c. White Pme. Yellow Pine. White Oak, Wrought spikes, c= 360 Wire nails, c= 167 Cut nails, c= 405 318 662 720 940 1216 Weight of Floors. Solid brick arched floors, 70 lbs. per sq.ft. Hollow brick arched floors, from 20 lbs. per sq. ft. for a 3 ft. span to 60 lbs. for a 10 ft. span. Wooden floors, lbs. per sq. ft. per inch of thickness: White Oak, 4; Maple, 3.5; Yellow- Pme, 3.2; White Pine and Spruce, 2.33 ; Hem- lock. 2. Floor Loads in lbs. per sq. ft. Street bridges, 80; dwellings, 40; churches, theatres and assembly rooms, 80; grain elevators, 100; ware- houses, 250; factories, 200 to 400. Prof. L. J. Johnson states as the result of experiments that the excessive crowding of adults may produce a load as high as 160 lbs. per sq. ft. 1 cu. ft. of brickwork gives a load of 115 lbs. '■q. ft. of supporting floor. (Masonry, 160 lbs.) MISCELLANEOUS TABLES AND DATA. 17 Roof I^ads in lbs. per sq. ft. Corniraited iron, 37 to 40; slate, 43 to 46 (add 10 lbs. if plastered below rafters). These values include an allowance of 30 lbs. for wind and snow. Snow per ft. depth, 6.4; maximum wind pressure, 50. Brick MasoniT* Common bricks are 8f in.X4* in.X2f in. Pressed. 8^ in.X4i in.X2| in. Wt., 5 to 6 lbs. Number of bricks per sq. ft. of wall surface = 1.55 X thickness of wall in inches (approx.). 1,000 closely stacked bricks occupy about 56 cu. ft. Safe load for brickwork in tons per sq. ft.: for good hme mortar, 8 tons; for good cement mortar, 15 tons. tN. Y. aty Law.) THE STRENGTH OF MATERIALS, STRUCTURES, AND MACHINE PARTS. Stress is the cohesive force within the material wtiioh is called into action to resist the load or externally applied force. Strain is the deformation produced by the stress and \a proportional to the stress within the elastic limit. Elasticity is the property which a body possesses of regaining its orig- inal shape and dimensions futer distortion. Modulus of Direct Elasticity JS; - ^ » ^. at Oe Modulus of Transverse Elasticity. C^/^-i-a, (forshear). Modulus of Tolumetric Elasticity. iC"/^-!- decrease in vcd. per ou. in. Elastic Moduli in Inch-pounds. Material. E C K Cast Steel 30,000,000 12.000,000 26,000,000 Forged Steel 30.000,000 13,000,000 26,000,000 Tempered Steel 36,000,000 14,000.000 W. I. Bars 29,000,000 10,500,000 20,000,000 •* Plates 26,000,000 14,000,000 20,000,000 Copper 12,000,000 24,000,000 ^^ rolled 15,000,000(fordrawn,E-17,000,000) Cast Iron 17,000,000 6,300,000 14.000.000 Brass and Gun Metal 13,500,000 15.000,000 Water 300,000 Poisson's Ratio (M). If a bar be extended or compressed, the direct strain (dt or Jc) = lateral strain (di)XM. The value of M for steel is 3.25, for W. I., 3.6, for C. I., 3.7, for copper, 2.6, and for brass, 3. Work. The unit of work is one foot-pound. Work = pressure or force X distance*- pounds X feet =ft.-lbs., and may be represented by the area of a figure with abscissae of distance and ordinates of pressure or force. Resilience -= the work done in deforming a body up to the elastic limit — F .^ J i-x lu total stress in lbs. ^ , « . . . * ^ ~Xi/ ft.-lbs. = 5 X deflection m feet. 8tress Due to Impulsive I^oad. Make energy equal to the resilience. Then, -jt-^-tti *"id F (lbs.) = —7, which is the maximum. The mean total stress (between and max.) =2ll7' ^^^^^ applies to steam-hammers, pile-drivers, etc. In case of a falling weight (e.g., sudden load on a beam or crane chain), w{h + Jff).^—^. Stress Caused by Heat. F='Eaea. Coefficients of Linear Expansion (a) per Deg. F. Tempered Steel 0000073 Cast Iron 0000062 Strong Steel 0000063 Brass 0000105 Mild Steel 0000057 Copper 0000095 Wrought Iron 0000066 Bronze 0000111 18 FACTORS OF SAFETY — ^STRESSES. 19 Belatlye Hardness of Materials, Cast steel, 564; brass. 233; mild steel, 143; aluminum (cast), 103; copper (annealed), 62; sine (cast), 41; lead, 4. Strenirth is Id creased as the temperature is lowered, — 50 to 100% at -295'' F. Iron and steel gain slightly in strength up to 500** F., but thereafter the decrease is rapid. Factors of Safety* Safe Load "Breaking Load -i- Factor of Safety. Dead live ^^7^^\ Load. Load.* ^lSSJI W. I and Mild Steel ... 3 5 to 8 9 to 13 Hard Steel 3 5 to 8 10 to 15 Bronses 5 6 to 9 10 to 15 C. I. and Brass 4 6 to 10 10 to 15 Masonry J ^^^ 20 to 30 Herr Wdhler's experiments in 1871 showed that range of rariation In stress was a factor in lowering the breaking load and also that rupture may be caused by repetitions and repeated reversals of stress, none of which attain the elastic limit. Prof. Unwin gives the following equation: /i— 2+'^//*--x57, where /i=the breaking stress under variation, in tons per sq. in., jS— stress variation in terms of A, 2:»1.5 for W. I. and mild steel and 2 for hard steel, and /"-breaking load under steady stress. „ ^ highest stress —lowest stress . , "" highest stress ** For a steady load /i=/; for a simple live or suddenly applied load, £»->/i; for alternately equal tensile and compressive stresses as in shaft- ing, iS«"2/i, whence, for W.L Steel. Steady load A-/ /i=/ Live load /1-O.6/ A-0.472/ Reversible load A=0.33/ A-0.26/ Or, safety factors are in the ratio 1 : 2: 3 to 4, approz. Average Breaking Stresses of Building Materials* (In lbs. per sq. in.) Material. Tension. Compression. White Oak 10,000 (I| to gram) 4,500 (columns < 15 Xdiam.) •• Pme 7,000 •••• " 3,500 La. Long-leaf Pine 12,000 '* " ** 5,000 Hemp Rope 8,000 Granite 600 16,000 Limestone 1,000 . 7,000 Sandstone 150 5,000 Stonework (0.4 X strength of stone used) Brickwork 50 1,000 (common, in lime mor- tar) ** 300 2,000 (best, m cement) Portland Cement, 1 mo. . 400 2,000 lyear. 500 3.000 Concrete, 1 mo. . 200 1,000 lyear 400 2.000 Rosendale Cement has about i the strength of Portland. Safe strengths of stone, brick, and cement —0.1 X breaking strengths. * A load on and off continually and instantly, but without velocity, t A reversible load causes alternate tension and compression. 20 STRENGTH OF BIATERIALS. Average Breaking Stresses of Blaterials and Safe Stresses for Ordinary Live Iioads. (In lbs. per sq« in*) Tension. Compression. Shear. Metals. Breaking. Safe. Break- ing. Safe. Break- ing. Safe. Crucible Cast Steel. Mild Steel Structural Steel. 0.1% Carbon.... Do., 0.15% C Soft Steel. 100,000 78.000 66,000 64,000 52-62.000 60-70,000 67,000 56,000 50,000 40.000 17,000 35,000 135.000 83,000 100,000 67.000 56,000 63,000 67,000 67,000 45,000 27,000 29,000 25;000 36,000 60,000 60,000 80,000 120,000 80,000 180,000 200,000 18.000 15.500 11,200 12,800 15,000 17.000 11,200 11,200 9,000 9,000 2,800 6,000 22.500 17,000 18,000 11,200 9.000 11,200 11,200 11,200 7,800 4,500 4,500 3,360 180.000 56.000 18.000 15.500 11,200 48,000 50,000 Webs- '45,666" 36,000 36,000 11,000 26,666" 11.200 11.200 9,000 10,000 (America Co. Pract 50.666 166,666 (14% Mn (Plates) (Forging 58,666 (anneaie (unanne (anneaie (unanne (anneaie (crucible (bridge c n Bridge ice.) 11,200 9,000 9,000 9,000 9,000 ) s) 11,200 9.000 s) 4,500 4,500 3,360 aled) aled) d) steel) able) 9000 Medium Steel Steel Castings Iron Forgings W.I. Plates II .... " + Cast Iron 10,000 7.800 7,800 6,700 6,700 2.200 7,800 6.700 3,360 3,360 MaUeable Iron. . . . Manganese Steel. .. Nickel Steel Manganese Bronae Phosphor Bronse . . Silicon Bronze. . . . Aluminum Bronze. Delta Metal Gun Metal. ...!!!! Copper Brass 2 200 Copper Wire Iron *• Steel ;; :::::: Note. Where vacancies occur in table, assume compression to eoual tension, and shear to be 0.7 X tension. || means parallel with grain or fiber, + means across grain. Tensile Stress-Action. Load = Total Stress, or w=fta, (=pXarea pressed upon in case of steam, air, or water pressure). Strength of Chain. w=14,00Qd^ lbs. for safe loading, where d^^diam. in in. of the wire in link. Wt. per ft, = lOcP, approx. (See Crane Chains, ante.) Strength of Ropes, w (safe) = 1,120^2 for White Hemp. For wire rope, ti;(safe)— 20,000rMp lbs., where n = no. of wires and (i = diam. of wire in in. (See Wire Kope, ante.) Strength of Pipes and Cylinders Pressed Internally. Thin Cylinders. For a longitudinal section (e.g., boiler) fi'^Y'' *°** for a transverse or ring section, /i = 5-. Stresses // must be multiplied by 9 in the case of boilers or other cylinders where welded, riveted, or bolted construction is used. In this case ij= efficiency = strength of joint + strength of solid platQ, For ordinary stefun, water, or gas pres- STRENGTH OP PIPES AND CYLINDERS. 21 etires, t>=0.18v^ for pipes and roush cyliiMlers. For maehining, in the case of cylinders, add 0.3 in. to above value of /. Kent states as an average' derived from a number of rules: /«=0.0004c{p+0.3 i&. Thick Cylinders. (For v ery h igh pressu res, e.g., hydraulic.) Exter- nal diam. = Internal diam. X V/« + p -^ v^i — p. Tensile Stress Induced by Centrifugal Force. /<— -. For oast Q iron w»B.261 lb. and U safe— 23001b. Placing these values in formula, V is found to be 170 ft. per sec., or the safe theoretical velocity of a fly- -wheel rim (double actual practice). StTength of Bolts. The working stress per sq. in. of cross-section at ^e bottom of thread for ordinary joints » 8,000 lbs. for W. I., and 11,000 lbs. for mild steel. (If under steam or water pressure, 6,000 lbs. In this case bolts <i in. should not be used and the pitch should not exceed 6d.) For steam cylinders, etc.. No. of tx^*a°2^( ^lt di^ ) '* ^^^ ^^*" have to resist shock the shanks should be turned down to the diam. at bottom of thread. Compressive Stress-Action, w = fdU. (Applicable where length < 12d.) (See Ooliunns.) Shear Stress- Action. For pins and rivets, w = fa. f safe =-11 ,000 lbs. per sq. in. (Am. Bridge Co. practice.) Strength of Eye Bars, ft safe- 14,000 to 16,000 lb. for soft and me- dium steel respectively. Proportions: D-d=«1.4&; d»| to U&: < (for 6<6 in.)=0.75 m.; « (for 6>5 in.)=(&+l)-!-8 (m.) Radius of fillet at neck =»D« outside diam. (Passaic R. M. Co.) 6=d=0.4i>, FiUet radius =Z). (Shaler Smith.) Strength of Riveted Joints. — Single-riveted Lap Joint. Shear strength of one rivet = tensile strength of plate between two holes, or /««<f2-H4 = /i(p"-d)< (1). d (of rivet) = 1.2 V7 before riveting; d«di (of hole) -1.3V^f after riveting (for plates <,1 in.). Subetitutmg in (1) and making /•» 11,200, /<» 13,500, pitch, p"-1.09+<2i for steel. For iron plates and rivets p"»= 1.14+di; for steel plates and iron rivets, p" = 0.76+ d\\ for copper plates and rivets p = 0.98 + di. (Supplee gives as standard practice (up to t in. plates) 1.31 and 1.25 in place of 1.14 and 0.76 as above.) Center of nvet to edge of plate = i overlap = 1.5rf. Pouble-riveted Lap Joint ( staggered or zig gag). p"-2.18+di. Dis- tance between rows of rivets = v^l.09di+0.75rfi2. Chain-riveted Lap Joint (double riveted, but not staggered), p"— 2. 18 -HA. Distance between rows » 1.5+ di. Double-riveted Butt Joint (with two cover plates). p" = 4.36+di. Diagonal distance between centers of rivets in the two rows = 2.18+di. Thickness of each butt strap or cover plate » \t of plate. Overlap — 2d. Treble-riveted Butt Joint. This case calls for three rows of rivets. The pitch of the third row from ed^ is twice the pitch of the first two rows, which are staggered Examinmg as a lap joint the metal between two holes on pitch line = (p"— d)— -~ — —the strength of one rivet. As 5 rivets have to be taken care of, then p"— -^ — - — —-{-di. Considered as a butt joint, (p"— d) = -^-T — , and for 6 rivets, p"'^ ' ^ +d\. An intermediate value is generally taken. (p"»= pitch of third row from edge of plate.) In the above formulas p" is taken equal to d} plus 2.18, 4.36, etc., which are miiltiples of 1.09 m formula for single-nveted lap joint, and are for steel plates and rivets where y " i^'sqq ' ^^^ other metals or combinations similar multiples of 1.14, 0.76, 0.98, etc., should be used, or, if other safe stresses are chosen for fa and ft, values of p" should be worked out from formula (1). Overlap =» If to 2d for treble-riveted butt joint, thickness of butt strap = It of plate. Rivet Proportions* Round or snap head: large diam. •• 1.67 X rivet 22 STRENGTH OP MATERIALS. diam, and height of head — |<f. Countersunk head: lange diam. — l|(f. and is coued to rivet shank at an ansle of 60^. Efficiency of Joints, ly— ^ ~ \ (Following table gives 9 for steel where /«-!-/«— 1.2.) <• rf. Singe-riv. I f .57 .54 ! X .49 1 li .45 li li .40 Double-riv. Double-riv. Treble-riv. Lap. Butt. Butt. .73 .84 .93 .70 .82 .92 .66 .79 .90 .62 .77 .90 .67 .73 .87 Riveting In Structural Worlc (example, — plate girder). Fhuice area a — TT. •*• Bm (neglecting bending stress on web) — oA/ (1). Bm of web — »*/ -T-, or allowing for rivet holes, ^-^"t and Bm (considering bending atie .» o o on web)=-A/(a + -g), and the flange area «"= "^ ~"^ (2)r Riveting: s Lower angles to web (in tension), neglecting Moment of Reedstance of web to bending; pitch of rivets, pf^'^hU-t- F, or the vertical shear . Upper angles to web, compression, M. of H. ne^ected; p'^=' V2-t-hM* ^^^^ u>— total loading per inch of length, p", A, < in in., a in sq. in., /• (=» least strength cf rivet subject to double shear and bear- */y^ ing stress) m lbs. per sq. in., V and w in lbs. The pitch of rivets Joining flange plates t< and near the ends of flanges, where p"-=4<i. he pitch of rivets Joining flange plates to angles is 6 in., excepting at Web stiffeners are angles riveted vertically to the web to prevent buck- ling of the latter. If f<gg the stiffeners should be spaced h in. apart (maximum spacing =60 in.). Pins, bolts, and rivets, unless fitting tightly and thoroughly gripping the plates, wiU be subject to bending stresses and smaller unit stresses must be employed, viz.: for circular sections, O.75/0; for square sections, 0.66/8; for square sections, forces acting along diagonal, 0.89/«. Strength of Cotter Joints. <;»diam. of rod =» breadth of cotter mid- way between ends = 4 X thickness of cotter. Taper of cotter 1 in 30 to 1 in 100. If tapered much greater than 1 in 30, cotters are apt to fly out. Torsional Stress-Action. External Moment = Moment of Resistance at section, or tn' — fsSt- Strensrih of Round Shafts. Moment of Resistance of section » 0.1964/a<f3 for solid shafts and 0.1964/a( ^^~ •) for hollow shafts. Strength of Square Shafts. Moment of Resistance of section «- 0.2Q8fa»^, where « = 8ide of square in in. Factor of Safety for Stiffness » 10 for short shafts; 16 for long shafts. Strength of Flange Coupling Bolts* ^ Diam. of bolt = 0.577>/(diam. of shaft )^-i- (bolt circle radius X No. of bolts). Strength of Sunk Keys. (Average practice.) Breadth^A (diam. of shaft) + A in.: Depth = i (diam. shaft) + i in.; Length = 0.3 (diam. shaft )^'(- depth. For splines or keys upon which parts rotating with shaft may also shde axiaily, interchange the above dimensions for breadth and depth. The Angle of Torsion, (0), is the angle through which one end of a shaft turns relatively to the other end under a given stress, (tf — arc -1- radius.) e = 2/«Z -H (d X Modulus of transverse elasticity, C). Strength of Helical Springs. For round wire, using shaft equation, trr-^/a^, where u>= axial pull in lbs., r = radius of coil (to center of wire CONICAL SPRINGS. BENDING STRESS. 23 section), /« (safe) = 60,000 (Begtrup and Hartnell). For square wire, t£v=0.208/«»*. Deflection -2/8/r-»-Cd, where i = 2jrrXNo. of turns or spirals, n; d=«diam. of wire, and C= 12,000,000. All dimensions in in. Further, deflection = 64Mmr'+C(i* for round-wire springs, and — e0.5umf*-i'C8* for square-wire. (Falues of f« and C are for steel wire.) Conical Springs, round wire. tpr=-^^, where r— largest radius of coil. I>enection =- . Flat volute (rectangular section of height h, breadth or thickness 6), tir-0.2226W.. Deflection = l:?^^H^^±^. Spiral Springs in Torsion. Round wire, ii;r=-»r/«d»-»-32. Deflection at r=^^^=/^. nEd* Square wire, ii;r=/««»-h6. '* ** r^ J^^ . (2 -» developed length of spring in inches.) Bending Stress- Action* In an overhung beam, or cantilever, the upi^r fibers are in a state of tension and the lower ones in compression, while in a supported beam, or girder, the opposite is the case. There exists therefore an intermediate longitudinal section where these stresses are zero in value. The intersection of this longitudinal section and a vertical cross-section is a line called the Neutral Axis, which passes through the center of figure (or gravity) of the cross-section. C!onsider two small areas, at and ae (distant yt and ^c from neutral axis), and let p be the radius of curvature of the neutral longitudinal section of the beam when under bending stress. Then, assuming the beam or bar to be bent into a cir- cular nng, I of bar (before bending) »=2jr|o; I (after bending), or circum- ference of bar at area a< = 2ir(/o-l-i/i), in tension, and I at area ae'^27t(p—Ve), in compression. Consequently, the strain on fibers at ai = 2n(p+yt)— 2xp^2xytt and strain at ae^2np—2n(p—ye)'^2itye; but ^^tt generally; .*. Zxy ' ' „ ^ ' and /— ~ (1), and the total stress on a small area o, Ja p Moment of Resistance. Moment of stress on the small area a— /aj/= — —^ and the moment of aU stresses on the section = —Joy^. Zay^^ p P Moment of Inertia of the section (or Second ]!4oment)-=/. .*. Moment of EI Resistance — — (2). Representing the moment in terms of the limiting stress, then. Bending Moment, Bm^/jS™ Moment of Resistance (3). S is called the Section Modulus (=■ virtual area X arm through which it acts). From (1), (2), and (3), 5-—, and Bm = ^. y y Moments of Inertia of Area. For Beams. Section. /. y(—dist. of furthest fil^ .' Rectangle, axis 11 to breadth and ^^^ *^s.) y. T. ,. bh» h bisecting section jo" Y Square, ditto, (6-A) ^ |- Square, axis bisecting section on diagonal r^ —g— (»— side of square.) 24 STRENGTH OF MATERIALS. Hollow rectangle or square, axis as for rectangle above Triangle, axis || to base Qrcle, diameter as axis bihi^-bh^ ^1 12 2 6*3 36 2h 3 64 d 2 * /A.4 ^4"^ di Hollow circle ^idi*-d*) D4 (&I, Ai, and di are outer dimensions.) For shafts. ( Polar Moment of Inertia —Ip.) Section. Ip. y. 12 2 Rectangle. Square. CSrcle. Hollow circle. 6 nd* 32 n{di*-d* ) 32 «^.V2= 0.707* •^ (rfi = outer diam. ) The Polar Moment of Inertia /p = / + /i, where / and h are two Moments of Inertia of the section which are taken at right angles to each other through the c. of g. of the section. The Radius of Gyration, r ~V- I, b--H| area of section* Moment of Resistance* Graphic Solution. AB is the neutral axis of the rectangular section CDHJ, and CD the line of limiting or greatest stress. The value of any horizontal fiber EF to resist stress is found by projecting the same vertically to the One CD and joining C and X) to N. The intercept GM is the value de- sired. All fibers being thus treated, the sum of the virtual stress areas will be the areas CDN and HJN which each make one force of the couple when multiplied by the limit- ing stress /. K and L are the cen- ters of gravity of the areas. Moment of Resistance of rectan- gular section = / (area CDN or HJN) Moment of Inertia of any Sec- tion. Find fS by above method, divide by value of / and multiply by y. (/ = <Si/. ) For rectangular sec - tion, S=-^, l^-= 2"' 12 Center of Gravity and Moment of Inertia Determined Graphic- ally (Fig. 3). Beam section 1 2 3 4 5 6 ... 12. To find center of grav- ity (considering right half of section): Project each horizontal fiber of section vertically to the arbitrarily assimied line xixy parallel to base line xx. Join ends of projection to point b and note the intercept on each fiber. The sum of all these fiber intercepts will be the area a 24 17 16 25 26 b a, or Ai. Then, A^h^AO, where A is area of right half of section (suflScient in case of sjnnmetry) and (? = distance of center of gravity from xx. Then. O'^Aih-i'A, which determines the position of neutral axis, zz. Pig. 2. MOMENT OF INEBTIA. 25 To find /of the section around 22 (considering left half of amotion) Project every horizontal fiber strip of section to II, the line of limiting stress, join ends of projeetion to point c (center of gravity) producing if necessary until the original strip is crossed, and note the intercepts. The areas 1 a e 14 13 1 (ai) and c 18 23 22 b c (aiO are thus found, and on opposite sides of verti- cal center line. They are the 1st moments. Gro through the same process as above with the areas oi and og', and the second moment areas 1 a c 15 14 1 Pig. 3. (os) and e 6 21 20 19 e (a«0 will be obtained, both being on the same side of vertical line. Then (doubling the results for the entire section). /=> / ,yt^ 2(02+02' )i/* and jS = — = 2(02 + 02' )i/. In cast-iron beams if fe— > ft , then ft y Vc is the limiting stress and the line II should be drawn at a distance yt from neutral axis. Position of Center of Gravity. The centers of gravity of regular figures (plane or solid) are the same as their geometrical centers. Triangle: i distance from middle of side to vertex of opposite angle. 26 STRENGTH OF MATERIALS. Trapezoid: divide into two triangles by a diagonal and join their centers of gravity; repeat process with the other diagonal and the in ie "faction of the lines joining the tenters of gravity ifdll be c. of g. of trapesoid. Sector of circle: on radius bisecting the arc. distance from center— (2 X chord X radius) -s- (3 X length of arc ). Semicircle: on middle radius, 0.4244r from center. Quadrant: on middle radius, 0.6002r from center. Segment of circle: distance from center = (chord )^+( 12 X area). . Parabola: f length from vertex, and on axis. Semi-parabola: | len^h from vertex, f semi-base from axis. Cone. Pyramid: m axis, i its length from base. Paraboloid: in axis, } its length from vertex. Frustum of Pyramid: distance from larger base = t ( 7=- ) • Frustum of Cone: *• ** •• "T V >;^^ Tp-l /• A "» height ; ^ , a, and A, r >- larger and smaller base areas and radii respeo- tively. Two or more bodies in the same plane: refer to co-ordinate axes. Mul- tiply the weight of each body by the distance from its center of gravity to one of the axes, add the products and divide by the sum of the weignts, the result being the distance of the center of gravitjr of the system from that axis. If bodies are not in a plane, refer them similarly to three rect- angular planes. Moment of Inertia of Compound Shapes. The Moment of Inertia of any section about any axis = the Moment of Inertia about a parallel axis passing through its center of gravity -h [area of section X( distance between axes)^]. Also, the Radius of Gvration for any section around an axis par- al lel to another axis through the center of gravity = V(dist. between axes )*+ (radius of gyration around axis through c. of g.)'. By these rules the / and r of "built up" beams and columns may be ob- tained, — for /, by finding the / of the several components of section about the same axis and adding the results for the combined section. Bendlne Moment and Deflection of Beams of Uniform Section. ( IT = total load on beam.) I. Beam fixed at one end, concentrated load at the other. Maximum Bfti at fixed end = Wl. (Bm iiuiy be represented by the ordinates of a right-angled triangle having base — I and height = Wl. ) Deflection = g^. II. Beam fixed at one end, uniformly distributed load (e.g., wt. of beam). Wl Max. Bfn at fixed end — -^. (Bm represented by ordinates from base of length 2 to a semi-parabolic curve having vertex at free end of 2 and axis l\ Wl' perpendicular thereto, and whose semi-parameter -» j^) . Deflection «= ^kTv* III. Beam, ends supported, concentrated load at center. Max. Bm at Wl Wl^ center = —r . Deflection = .-p. . IV. Beam, ends supported, concentrated load at any point. Max. Bm— W(l — x)x — ^ — —t where 2; » distance of load from one support. Deflection— WxHl-x)^ SEIl • Wl V. Beam, ends supported, uniform load. Max. Bm at center*-—-. Deflection =^jg^^. VI. Beam fixed at both ends, centrally loaded. Max. Bm at center and Wl Wl^ I ends = -^. Deflection =£02^7' Points of contra-flexure distant — from ends. VII. Beam fixed at both ends, imiformly loaded. Max Bm at ends=> STRENGTH AND DEFLECTION OF -BEAMS. 27 Wl (Wl ^ ^ \ 0.2112 from ends. Deflection = 384Er Points of contra-flexure are VIII. Beam fixed at one end, jupported at the othf ^^^ uniformly Point of con- 'upi _ loaded. Max. Bm. at fixed end=-^. Deflection -•rg^^, tra-flexure=-7- from fixed end. IX. Beam fixed at one end, supported at the other, and centrally loaded. Max. Bm 16 • Deflection -» appoi 7Q8EI' W X. Beam loaded at each end with -^, with two supports, each distant x from ends. Max. Bm^ Wx Deflection, overhang," Wx(l-2x)^ 16EJ Wx(3lx-4x^) 12EJ for middle part, — XI. Beam, both ends supported, with two ssrmmetrically placed loads (each^-r-), each x dist. from support. Max. Bnt^-^-. Deflection — W^x(3P-4x») 48EI • XII. Beam, fixed at one end, distributed load increasing uniformly from towards fixed end. Max. Bm = "o"* Deflection — ..pj . -:L_._ i ^ Fifi:.4. XIII. Beam, both ends supported, distributed load increasing Wl from at center towards ends. Max. Bm^-jo"- Deflection ^ oonKT ' XIV. Same as XIII, but with load increasing imiformly from O at to oeDter. Max. Bwi = -g-« Deflection QOEI' 28 STRENGTH OF MATERIALS. XV. Beam overhangi^ each of two supports by distance x, umformly distributed load. Bfn= -^j- at either support, and -^iz—0J25l) at center. UaxBm (when a;-0.2070- j~. Combinations of loading may be shown graphically as in Fig. 4. Tr» uniform load, and IT; = concentrated load. Consider the beam as merely supported at the ends, with a imiform load (e.g., itself). Then, the par- W2 abola AFBt on base AB, and of height«=-^, is the curve of Bm for W, A^ain, conader beam as loaded only with Wi. Then, the triangle AOB will be the curve of Bfn for TTi.and, by adding the ordinates of these curves a new curve AHEIB is obtained, wluch is the curve of Bm, for the com- bined loads on a freely supported beam. Again, consider the beam as fixed. The Bm of the supported beam is now opposed by the reaction of the wall, which is a constant strain and whose Bm curve is the rectai^e ACDB, equal in area to AH BIB, The algebraic sum of these bending moments gives for the fixed beam the shaded Bm curve ACHEIDBIHA^ and the intersections at H and / determine the points of contra-flexure. The portions CH and ID are strained as cantilevers, the upper sides bein^ in tension, while the part HI is strained as a supported girder, with tension on lower side. The Bm curve for a moving load (e.g., that on a travelling-crane girder) is Wl IMurabolic, with a maximum at center equal to --t-. 4 Shear Stresses, The vertieal shear stress caused by a concentrated load is represented by the ordinates of a rectangular area having a length « dist. from point of support to point of max. Bm* and a height — reaction at point of support. The vert, shear stress caused by a uniformly dis- tributed load IS represented by the ordinates of a right-angled triangular area having base as above* and height at point of support = reaction at that point. Thus, in Fig. 6, rectangles 1 2<8 4 and 2 5 6 7 IS are for concentrated load W\ (see fig. 4), and triangles 18 9 and 9 10 7 for distrib- uted load PT. The algebraic sum of these areas gives areas 1 11 12 and 12 13 14 15 7 12, any ordinate of which shows the vertical shear stress of the combined loads at the point where ordinate is erected. Heights 1 4, 6 7 and 111, 7 15 represent the reactions or proportions of Wx and W respectively sustained by the points of support. Horizontal shear stress* If a summation of the hori- Bontal forces (tensile and com- pressive) is taken, proceeding from the upper or lower fibre to the neutral axis, it will be found that the max. hor. shear stress is at the neutral axis, and, in a rectangular beam, at any section: Max. hor. shear stress — (3 X Vert, shear at the section considered) + 26d, where h and d are breadth and depth of beam. In long beams the shear is small compared with the bending stress and is fully taken care of by the surplus section ; in short beams it should be considered. Continuous Beams. (Reactions on supports in terms of TTi, the uni- form load on each span.) COMBINED STRESSES. 29 3 atipporti 3 4 11 16 41 56 152 209 10 11 32 43 lis 161 440 GOl 3 U 2B 37 lOS 137 374 511 ftfijf h X W'l + 8 5 4 32 37 loe 143 11 43 108 143 529 " '* + 10 " '* + 28 6 ■* 7 15 158 137 529 41 Ifll 374 .'>,35 " '' ^ 38 " ** +104 8 " 9 *' 10 " 5fi 440 511 152 001 209 ** *' -J- 142 " * +38S " " -=-530 The Allowable Deflection for cantileven is ^ in. per foot of span, and itf in. per ft. of span for girders. Beams of Uniform Strength (Rectangnlar Section). — ^V^th constant breadth, the depth varies as the ordinates of: I, a semi-parabola with ver^ tex at loaded end; II, a triangle, base at fixed end: III and IV, two semi- parabolas, vertices at supports, bases joining at load point; V, a semi- ellipse. With constant depth the breadth varies as the ordinates of: I. a triangle, base at fixed end; II, distance between two convex parabolas whose vertices touch at free end ; III and IV, two triangles, bases at load point: V, distance between two sjrmmetrical concave parabolas intersect- ing at points of support. (I, II, III, etc., refer to conditions of loading under the heading of Bending Moment and Deflection of Beams, ante.) Stren^ of Circular Flat Plates of Radius r (Grashof).— Plate sup- ported at circumference and uniformly loaded: /—0.833pr' -»-<'. Sameload- mg, plate fixed at circumference: f=0.Q66pr^+f< Plate supported at cir- cumference, loaded centrally with w (of radiusri) : /— (l.383 ^<>8 ^ + 1)*^ . Strength of Square and Rectangular Flat Plates, Uniformly Loaded (Unwm).— Rectangular plate, fixed at edges: f'-0.5m*p-t-(b*+l*)t''i, where 6 => breadth and ^ = length of plate in in. Square plate, fixed at edges: /=0.25p« -Hf'', where « = side in in. Surface supported by stays: /— 0.222p8 +f'*, where «»» distance in in. between the cenj«rs of stays, wmch are arranged in rows, /^working stress in lbs. Strength of Flat Stayed Surfaces. (See Steam BoUers.) fnbfi Strength of LAmlnated Steel Springs, u^- 61 fP Deflection, i-~, where to— max. static load on one end of a semi-elliptic, or \ max. load on full elliptic spring; /= allowable stress in lbs. per sq. in. (varying accord- ing to homogeneity and temper) — 90,000 for i-in. plates, 80,000 for f-in., and 75,000 for Hn.; n=no. of plates; ! = half span in ins.; ^=30,000,000. (Reuleaux and Gaines.) Combined Stresses. Bending and Tension (Load parallel to aris at distance r). — Bending action = w=/riS=-/|cS; tensile action =u;»=/ia. Oombined max. tensile stress on edge nearest axis of wft'='w( — ^~^)* (^^ Modulus of Rup- ture.) Strength of Crane Hooks. w=abffi-Ct where a « radius of insido of hook or sling, A = breadth of hook on nor. section through center of inside hook circle, & = thickness of section, 17,000 lbs. Values of C: w»load in lbs., ft safe -13,000 to Rectang;ular secti<»i, Trapeeoidal section. Elliptical " h-^-a^ 1 1.5 2 2.5 3 4 C-12.6 7.25 6.07 8.92 3.22 2.41 C=15 8.96 6.42 5.06 4.18 3.28 C=21.5 12.68 8.89 6.92 5.73 Distance from center of hook circle to shoulder on bolt end =» 2h. Diam. of bolt end di = i 4,267 be next to rope or chain; narrow edge &i-» 6 -h T — \-lj In trapezoidal sections, the wide edge b should h_ a (Ing. Taschenbuch). 90 8VRENOTH OF MATERIALS. Towne eLvee the foUowing proportions: Neck— d (taken as unit): turned shank —0.87^; sling diam.="1.6o<2; diam. of tip on hor. diam. of sling — 0.7(2; radial width of flattened wedge section on hor. sling diam. — 1.4<2; thickness of inner wedge edge— 0.875d; do., outer edge— 0.26d; width at mouth of sling -1.25d. SiJe dead load in lbs.-l,500d2, where d is in inches. Reuleaux gives the following: 2a-1.95d, -0.039'viy-A-1.56 = 2Xdiam of hook tip on hor. line through c. of hook sling, — 1.33 X width at hook opening. These values agree fairly well with the Taschenbuch formulas (taking /« - 1 3,000) . /Compare with formula ft'^^C'^'^^j) Bending and Compression* Substitute /« for ft in formiilas for bend- ing and tension. Example: ship's davits. Columns and Struts. While these are cases in volvingl bending and compression, their action is more complex. Where l<l2a they are cal- culated for direct crushing only; longer columns bend before breakini;. Gordon's Formulas* / hresVing - — ^-^. both ends fixed or flat ; V one end fixed, other! 1 + 1.86 f— ) i"Wd or round; l+45(^ rounds both ends hinged or where l^length in Ins., vleati radius of gyratum, and a and h an as follows: a. b. Castlron 80,000 g-^ W. I. and very soft steeL . 86,000-40,000 ^qoqo *® 40.OO6 Medium SteeL.... 67,000 Hard SteeL 114,000 Dry Timber. 7,200 SoftSteeL". f 15,000 MediumSteeL I 17,000 22,400 siooo 13^500 ii;ooo . Am. Bridce Co. Praotioe. Safe values. section in sq. in. TK«. ../n^\ / (breaking) in lbs, per sq. in. X area of Then, w (lbs.) Factor of safety. For W. I. and steel, factor of safety— 4 for dead load, and 6 for moving load. For C. I. not less than 8. Prof. Lanza states as the result of experiments that Gordon's formulas do not SLPply in the case of cast-iron columns, and he recommends 5,000 lbs. per sq. in. as the highest allowable safe loading, the length of column not to exceed 20 times its diameter and the metal to be of thickness suffi- cient to insure sound castings. Eccentric Ix>adlnflf. When the resultant of the load does not pass through the c. of g. of the section, let r— distance between resultant and c. of g. of section ; / its moment of inertia about an axis in its plane pass- ing throu^ the c. of g. and perpendicidar to r; {/—distance between said axis and nbre under greatest compression; tt'— total pressure on section. Then /— — + — 7— Assume a section, compute /, and if it exceeds safe value (5,000 for C. I.) assume another section and compute / until a safe CABNEGIE ROLLED STRUCTURAL STEEL. 31 value is found. Eccentric loading in buildings is due to the unequal dis^ tribution of loads on floors. If liable to occur only in rare cases, / may be taken at 8,000 lb. per sq. in. for C. I. Safe Loads for Bound and Square Cast Iron Columns* (City Building Laws, 1807.) Safe load in tons of 2,000 lb.« ^\ . New York. Boston. Chicago. C (round or sq.) = 8 6 5 5(square) =500 1.067 800 5 (round) =400 800 600 Resistance of Hollow Cylinders to Collapse. (See Furnace Flues under *'Steam Boilers.") Torsion and Bendine. This combination of stresses exists to a greater or less extent in all shsJting. Equivale nt twisting moment =2 Xequivar lent bending moment =jBw»+'^B»»2+Tto^ where 7*^= twisting moment— Torsion and Compression. (Propeller shaft.) w*=— ^ 4^ A safety factor of 5 should be used. Modulus of Rupture. The ultimate stress obtained from the momental formula in breaking a solid beam by bending will usually be found much greater than ft bres^ing. " Modulus of Rupture h'^cfu where c generally =2 for circular and square (one diagonal vertical) sections, 1.5 for square and rectangular sections, and unity for I and T sections. The values of e depend however on the material: Rectangular sections; Fir, 0.52 to 0.94; Oii, 0.7 to 1; Pitch-pine, 0.8 to 2.2; C. I., 2; W. I.. 1.6; Forged steel, 1.47; Gun metal, 1. Circular sections: C. I., 2.35; W. I., 1.75; Forged steel, 1.6; Gun metal, 1.9. I sections: C. I., l+(web thickness •»- flange width)., CARNEGIE ROLLED STRUCTURAL STEEL. In the following tables, u;= weight in lbs. per lineal foot, a » area of sec- tion in sq. in., A » depth of beam or channel in in., &» width of flange in in., <» thickness of web in in. X9 xu xs"' distance between o. of g. of section and (1) outside of channel web; (2) outside of flange on T; (3) back of flange of equal leg angle. /, r« jSf— Moment of inertia, radius of gyration and section modulus, where Neutral axis is perpendicular to web at center (Beams and chan- nels). ' parallel to longer flange (Unequal leg angles). ** '* " through c. of g. paral^l to flange (Ts and equal leg - angles). •• •* •• ohrough c. of g. perpendicular to web (Zs). V9 f'"- Moment of inertia and radius of gyration, where Neutral axis is coincident with center line of web (Beams). " '* parallel to center line of web (Channels). «• •« '* ** '* shorter flange (Unequal leg angles). '* through c. of g. coincident with stem (Ts). " •• *• ** ** V , •* web(Zs). r^M Least radius of gyration, neutral axis diagonaL flf'*- Section modulus, where Neutral axis is through c. of g. coincident with stem (Ts). *• •• •* •• web(Zs). *' <• •< parallel to shorter flange (Unequal leg angles^. C» Coefficient of strength for fibre stress of 16,000 lbs. per sq. m. for beams, channels, and Zs, and 12,000 lbs. per sq. in. tor Ts. C - TTL - 8 Jf=~-, where/ =12,000 to 16,000 lbs.; Af«= moment of forces in ft.-lbs., TT^safe uniformly distributed load in lbs., £»span in feet. For concentrated load at middle of span use one-half the value of C in the tables. For quiescent loads /= 16,000 lbs. per sq. in.; for moving loads, 12,500 lbs., and, if impact is considerable, /= 8.000 lbs. For columns or struts consisting of two latticed channels, r of column jection (neut. axis in center of section U to webs) »» distance between c. of g. 32 STRENGTH OF MATERIALS. f]/t channel and center of column section (ne^^ecting tbe Ib dt chaanelfl around their own axes, — a slisrht error on the safe side). Camegrie Steel I Beams. (Sizes with * prefixed are standard, others are speeial.) h. w. «• t. 6. /. /'. r. ^^ s. C. 24 in. 100 29.41 0.75 7.26 2380.3 48.56 9 1.28 198.4 2116800 95 27.94 .69 7.19 2309.6 47.1 9.09 1.3 192.6 2062900 90 26.47 .63 7.13 2239.1 45.7 9.2 1.31 186.6 1990300 85 25 .57 7.07 2168.6 44.36 9.31 1.33 180.7 1927600 * 80 23.32 .50 7 2087.9 42.86 9.46 1.36 174 1865900 ao 100 29.41 .88 7.28 1665.8 62.65 7.6 1.34 166.6 1706100 95 27.04 .81 7.21 1606.8 60.78 7.68 1.36 160.7 1713900 90 26.47 .74 7.14 1557.8 48.98 7.67 1.36 166.8 1661600 85 25 .66 7.06 1508.7 47.26 7.77 1.37 150 9 1600300 • 80 23.73 .60 7 1466.6 45.81 7.86 1.39 146.7 1564300 75 22.06 .65 6.40 1268.9 30.25 7.58 1.17 126.9 1353600 70 20.59 .58 6.32 1219.9 29.04 7.7 1.19 122 1301200 * 65 19.08 .50 6.26 1169.6 27.86 7.83 1.21 117 1247600 28 70 20.59 .72 6.26 921.3 24.62 6.69 1.09 102.4 1091000 65 19.12 .64 6.18 881.6 23.47 6.79 1.11 97.9 1044800 60 17.65 .56 6.09 841.8 22.38 6.91 1.13 93.5 097700 * 65 15.93 .46 6 795.6 21.19 7.07 1.15 88.4 943000 15 100 29.41 1.18 6.77 900.6 50.98 6.63 1.31 120.1 1280700 95 27.94 1.09 6.68 872.9 48.37 5.69 1.32 116.4 1241600 90 26.47 .99 6.68 846.4 45.91 6.65 1.32 112.7 1202300 85 25 .89 6.48 817.8 43.57 6.72 1.32 109 1163000 • 80 23.81 .81 6.4 795.6 41.76 6.78 1.32 106.1 1131300 75 22.06 .88 6.29 691.2 30.68 6.60 1.18 92.2 983000 70 20.59 .78 6.19 663.6 29 6.68 1.19 88.5 943800 65 19.12 .69 6.1 636 27.42 6.77 1.2 84.8 904600 • 60 17.67 .69 6 609 26.96 6.87 1.21 81.2 866100 55 16.18 .66 6.76 611 17.06 6.62 1.02 68.1 726800 50 14.71 .56 6.65 483.4 16.04 6.73 1.04 64.6 687500 45 13.24 .46 5.65 456.8 16.00 6.87 1.07 60.8 648200 * 42 12.48 .41 6.5 441.7 14.62 6.96 1.08 68.9 628300 12 55 16.18 .82 5.61 321 17.46 4.45 1.04 53.5 670600 50 14.71 .70 6.49 303.3 16.12 4.54 1.05 50.6 639200 45 13.24 .58 6.37 285.7 14.89 4.65 1.06 47.6 607900 * 40 11.84 .46 5.26 268.9 13.81 4.77 1.08 44.8 478100 35 10.29 .44 6.09 228.3 10.07 4.71 .99 38 405800 * 31.5 9.26 .35 6 216.8 9.60 4.83 1.01 36 383700 10 40 11.76 .76 5.10 168.7 9.60 3.67 .90 31.7 338500 35 10.29 .60 4.96 146.4 8.62 3.77 .91 29.3 26.8 312400 30 8.82 .46 4.8 134.2 7.66 3.9 .93 286300 * 25 7.37 .31 4.66 122.1 6.89 4.07 .97 24.4 260600 9 35 10.29 .73 4.77 111.8 7.31 3.29 .84 24.8 265000 30 8.82 .67 4.61 101.9 6.42 3.4 .85 22.6 241500 25 7.35 .41 4.45 91.9 5.65 3.54 .88 20.4 217900 * 21 6.31 .29 4.33 84.9 6.16 3.67 .90 18.9 201300 8 25.6 7.50 .64 4.27 68.4 4.76 3.02 .80 17.1 182500 23 6.76 .45 4.18 64.6 4.39 3.09 .81 16.1 172000 20.5 6.03 .36 4.09 60.6 4.07 3.17 .82 15.1 161600 * 18 5.33 .27 4 66.9 3.78 3.27 .84 14.2 151700 7 20 5.88 .46 3.87 42.2 3.24 2.68 .74 12.1 128600 17.5 5.16 .35 3.76 39.2 2.94 2.76 .76 11.2 119400 * 15 4.42 .25 3.66 36.2 2.67 2.86 .78 10.4 110400 6 17^ 5.07 .48 3.68 26.2 2.36 2.27 .68 8.7 93100 14 4.34 .35 3.46 24 2.09 2.36 .69 8 86300 • 12 3.61 .23 3.33 21.8 1.85 2.46 .72 7.3 77600 6 14 4.34 .60 3.29 16.2 1.7 1.87 .63 6.1 64600 12 3.60 .36 3.16 13.6 1.45 1.94 .63 5.4 58100 • 9 2.87 .21 3 12.1 1.23 2.05 .66 4.8 51600 CABNSGIB BOLLED STRUCTSIUIi SfTESSU 33 Camegle Steel I 'Beams.— ConHntted, h. v>. a. U h. /. /'. r. r*. 8. C. 4 In. 10.5 3.09 .41 2.88 7.1 1.01 1.52 .67 3.6 38100 9.5 2.79 .34 2.8 6.7 0.03 1.55 .68 3.4 36000 8.5 2.5 .26 2.73 6.4 .85 1.69 .58 3.2 33900 m 7.6 2.21 .19 2.66 6 .77 1.64 .69 3 31800 3 7.5 2.21 .36 2.52 2.9 .60 1.16 .52 1.9 20700 6.5 1.91 .26 2.42 2.7 .63 1.19 .52 1.8 19100 m 6.5 1.83 .17 2.33 L2.6 .46 1.23 .63 1.7 17600 Camegle Steel Channels* (Siiesjwith * prefixed are standard, others are spedaL) K IT. a. U 6. /. /'. r. t*. S. C. «. ism. 55 16.18 0.82 3.82 430.2 12.19 5.16 0.868 67.4 611900 0.823 50 14.71 .72 3.72 402.7 11.22 5.23 .873 53.7 672700 .803 45 13.24 .62 3.62 375.1 10.29 6.32 .882 50 533500 .788 40 11.76 .62 3.52 347.5 9.39 5.43 .893 46.3 494200 .783 35 10.29 .43 3.43 320 8.48 5.68 .908 42.7 455000 .789 m 33 9.9 .40 3.40 312.6 8.23 6.62 .912 41.7 444500 .794 12 40 11.76 .76 3.42 197 6.63 4.09 .761 32.8 350200 .722 35 10.29 .64 3.3 179.3 6.9 4.17 .767 29.9 318800 .694 30 8.82 .51 3.17 161.7 5.21 4.28 .768 26.9 287400 .677 25 7.35 .39 3.05 144 4.63 4.43 .785 24 266100 .678 m 20.5 6.03 .28 2.94 128.1 3.91 4.61 .806 21.4 227800 .704 10 35 10.29 .82 3.18 116.5 103.2 4.66 3.35 .672 23.1 246400 .695 30 8.82 .68 3.04 3.90 3.42 .672 20.6 220300 .661 25 7.35 .53 2.89 91 3.40 3.62 .680 18.2 194100 .62 20 6.88 .38 2.74 78.7 2.85 3.66 .696 15.7 168000 .609 « 15 4.46 .24 2.6 66.9 2.30 3.87 .718 13.4 142700 .639 9 25 7.35 .62 2.82 70.7 2.98 3.10 .637 15.7 167600 .615 20 5.88 .46 2.65 60.8 2.45 3.21 .646 13.5 144100 .586 15 4.41 .29 2.49 50.9 1.95 3.40 .665 11.3 120600 .69 « 13i 3.89 .23 2.43 47.3 1.77 3.49 .674 10.6 112200 .607 8 2\\ 6.26 .68 2.62 47.8 2.26 2.77 .6 11.9 127400 .587 18} 6.51 .49 2.53 43.8 2.01 2.82 .603 11 116900 .567 16| 4.78 .40 2.44 39.9 1.78 2.89 .610 10 106400 .656 13 4.04 .31 2.36 36 1.55 2.98 .619 9 96000 .667 m 11 3.35 .22 2.26 32.3 1.33 3.11 .63 8.1 86100 .576 7 19 5.81 .63 2.51 33.2 1.85 2.39 .665 9.6 101100 .683 17 6.07 .63 2.41 30.2 1.62 2.44 .664 8.6 92000 656 14 4.34 .42 2.3 27.2 1.40 2.50 .668 7.8 82800 .535 12 3.60 .32 2.2 24.2 1.19 2.69 .576 6.9 73700 .628 « 9| 2.86 .21 2.09 21.1 .98 2.72 .686 6 66800 .646 6 15 6 4.56 .66 2.28 19.6 1.28 2.07 .529 6.6 69600 .546 13 3.82 .44 2.16 17.3 1.07 2.13 .529 6.8 61600 .517 10.5 3.09 .32 2.04 15.1 .88 2.21 .634 5 53800 .603 « 8 2.38 .20 1.92 13 .70 2.34 .542 4.3 46200 .517 5 11.5 3.38 .48 2.04 10.4 .82 1.75 .493 4.2 44400 .508 9 2.66 .33 1.89 8.9 .64 1.83 .493 3.6 37900 .481 « 6.5 1.95 .19 1.75 7.4 .48 1.96 .498 3 31600 .489 4 7 2.13 .33 1.73 4.6 .44 1.46 .456 2.3 24400 .463 6 1.84 .25 1.66 4.2 .38 1.61 .454 2.1 22300 .458 m 5: 1.56 .18 1.68 3.8 .32 1.56 .463 1.9 20200 .464 3 6 1.76 .36 1.6 2.1 .31 1.08 .421 1.4 14700 .45§ 5 1.47 .26 1.5 1.8 .25 1.12 .415 1.2 13100 .443 • 4 1.19 .17 1.41 1.6 .20 1.17 .409 1.1 11600 .443 34 STRENGTH OF MATERIALS. Carnegie T Shapes (Selected). Flange XStem, ias. w. a. xu /. S. r. /'. S\ r'. C. 4X5 15.7 4.56 1.56 10.7 3.10 1.54 2.8 1.41 0.79 24800 4X5 12.3 3.54 1.51 8.5 2.43 1.56 2.1 1.06 .78 19410 4X4i 14.8 4.29 1.37 8 2.55 1.37 2.8 1.41 .81 20400 4X4 13.9 4.02 1.18 5.7 2.02 1.2 2.8 1.4 .84 16170 3X4 10.6 3.12 1.32 4.8 1.78 1.25 1.09 .72 .60 14270 3X4 9.3 2.73 1.29 4.3 1.57 1.26 .93 .62 .59 12540 3X3* 3X3i 9.8 2.88 1.11 3.3 1.37 1.08 1.31 .88 .68 10990 8.6 2.49 1.09 2.9 1.21 1.09 .93 .62 .61 9680 3X3 9 2.67 .92 2.1 1.01 .9 1.08 .72 .64 8110 2iX3 6.2 1.8 .92 1.6 .76 .94 .44 .35 .51 6110 2iX2f 2iX2r 5.9 1.71 . .83 1.2 .6 .83 .44 .35 .61 4830 5.6 1.62 .74 .87 .5 .74 .44 .35 .62 4000 2ix2 2iX2 6 1.44 .69 .66 .42 .68 .33 .30 .48 3360 4.2 1.2 .66 .51 .32 .67 .25 .22 .47 2600 2X2 3.7 1.08 .59 .36 .25 .6 .18 .18 .42 2000 ifxif 3.2 .9 .54 .23 .19 .51 .12 .14 .37 1540 ijxi- Uxi 2.6 .75 .42 .15 .14 .49 .08 .10 .34 1150 2 .64 .44 .11 .11 .45 .06 .07 .31 860 Uxi 2.1 .60 .40 .08 .10 .36 .05 .07 .27 760 XI 1.23 .36 .32 .03 .05 .29 .02 .04 .21 370 1X1 0.87 .26 .29 .02 .03 .29 .01 .02 .21 270 Carnegrle Steel Angles with Equal Legs a Max. and Min. Wts. Special Sizes marked * Biae. L u\ a. X2. / S. r. r". 8X8 1 ; 5e,9 ie.73 2.41 97.97 17.53 2.42 1.55 8X8 2(> 4 7.75 2.19 48.63 8.37 2.5 1.58 6X6 1 :^7.4 11 1.86 35.46 8.57 1.8 1.16 6X6 f 14 9 4.36 1.64 15.39 3.53 1.88 1.19 •5X5 1 ao t> 1.61 19.64 5.8 1.48 0.96 *fix5 1 12 :i 3.01 1.39 8.74 2.42 1.56 .99 4X4 4 ]0 9 5 84 1.29 8.14 3.01 1.18 .77 4X4 ' v K.2 2.4 1.12 3.71 1.29 1.24 .79 34X3* 1 17,1 5.03 1.17 5.25 2.25 1.02 .67 3*X3* t 7.2 2 09 .99 2.45 .98 1.08 .69 3X3 Jl.fi 3.36 .98 2.62 1.3 .88 .57 3X3 ^ 4.fl 1.44 .84 1.24 .58 .93 .59 •aix2i: f 8.fl 2.5 .87 1.67 .89 .82 .52 4,5 1.31 .78 .93 .48 .85 .65 2^X3^ 7.7 2.25 .81 1.23 .73 .74 .47 3*X2. > aj ,9 .69 .55 .30 .78 .49 *2 X2 ; B.N 2 .74 .87 .58 .66 .43 *2ix2: ^ 2.R .81 .63 .39 .24 .70 .44 2x2 T* 5 ;^ 1.56 .66 .54 .40 .59 .39 2X2 nX- 2.5 .72 .57 .28 .19 .62 .40 UxiJ rt 4 6 1,3 .59 .35 .30 .51 .33 lixi J^ 2 2 A\2 .51 .18 .14 .54 .35 14 X 1 3.4 .09 .51 .19 .19 .44 .29 UXI n . 1.3 .36 .42 .08 .07 .46 .30 Hxi A 2 4 .69 .42 .09 .109 .36 .23 1 Xl : 1.1 .3 .35 .044 .049 .38 .25 :xi i 1.5 .44 .34 .037 .056 .29 .19 xl .8 24 .3 .022 .031 .31 .20 •4X A lAi ,29 .29 .019 .033 .26 .18 .. X' .7 .21 .26 .014 .023 .26 .19 X ■ % .9 .25 .26 .012 .024 .22 .16 ■■X- .6 .17 .23 .009 .017 .23 .17 CABNEGIE ROLLED STRUCTURAL STEEL. 35 Carnegie Steel Angles with Unequal Legs* Max. and Min. Wts. Special Sizes marked *. Size. /. w. a. /. /'. S' . S\ r. r'. r" *8X3^ ii 20.5 6.02 4.92 39.96 1.79 7.99 0.9 2.58 0.74 *7X3i 1 32.3 9.5 7.53 45.37 2.96 10.58 .89 2.19 .88 *7X3i ^ 15 4.4 3.95 22.56 1.47 5.01 .95 2.26 .89 6X4 1 30.6 9 10.75 30.75 3.79 8.02 1.09 1.86 .86 6X4 f 12.3 3.61 4.9 13.47 1.6 3.32 1.17 1.93 .88 6X3i 1 28.9 8.5 7.21 29.24 2.9 7.83 .92 1.86 .74 6X3i 1 11.7 3.42 3.34 12.86 1.23 3.25 .99 1.94 .77 *5X4 24.2 7.11 9.23 16.42 3.31 4.99 1.14 1.52 .84 *5X4 . 11 3.23 4.67 8.14 1.57 2.34 1.2 1.59 .86 6X3i 5X3i 22.7 6.67 6.21 15.67 2.52 4.88 .96 1.53 .75 JL 8.7 2.56 2.72 6.6 1.02 1.94 1.03 1.61 .76 6X3 . . 19.9 5.84 3.71 13.98 1.74 4.45 .80 1.55 .64 5X3 A 8.2 2.4 1.75 6.26 .75 1.89 .85 1.61 .66 *4iX3 *4iX3 ■ . . 18.5 5.43 3.6 10.33 1.71 3.62 .81 1.38 .64 A 7.7 2.25 1.73 4.69 .76 1.54 .88 1.44 .66 *4X3^ 18.5 5.43 6.49 7.77 2.30 2.92 1.01 1.19 .72 *4X3i jy 7.7 2.25 2.59 3.56 1.01 1.26 1.07 1.26 .73 4X3 if 17.1 5.03 3.47 7.34 1.68 2.87 .83 1.21 .64 4X3 A 7.2 2.09 1.65 3.38 .74 1.23 .89 1.27 .66 3*X3 Tf 15.8 4.62 3.33 4.98 1.65 2.20 .85 1.04 .62 3iX3 s 6.6 1.93 1.58 2.33 .72 .96 .90 1.1 .63 3iX2i 12.5 3.65 1.72 4.13 .99 1.85 .67 1.06 .63 3^X2^ r 4.9 1.44 .78 1.80 .41 .75 .74 1.12 .64 *3iX2 A 9 2.64 .75 2.64 .53 1.30 .53 1 .44 *3iX2 4.3 1.25 .4 1.36 .26 .63 .57 1.04 .46 3X2i A 9.5 2.78 1.42 2.28 .82 1.15 .72 .91 .62 3X2i 4.5 1.31 .74 1.17 .40 .56 .75 .95 .63 *3X2 , . 7.7 2.25 .67 1.92 .47 1.00 .55 .92 .43 *3X2 . . 4.1 1.19 .39 1.09 .25 .54 .57 .95 .43 2^X2 6.8 2 .64 1.14 .46 .70 .56 .75 .42 2^X2 *2iXH *2iXU *2Xlf *2Xli A 2.8 .81 .29 .51 .20 .29 .60 .79 .43 5.6 1.63 .26 .75 .26 .54 .40 .68 .39 A 2.3 .67 .12 .34 .11 .23 .43 .72 .40 2.7 .78 .12 .37 .12 .23 .39 .63 .30 ^ 2.1 .60 .09 .24 .09 .18 .40 .63 .31 *lfXl *ifxi 1.9 .53 .04 .09 .05 .09 .27 .41 .22 i 1 .28 .02 .05 .03 .06 .29 .44 .22 Carnegie Steel Z Bars. (Dimensions: thickness X width of flange X depth of web.) Dimensions. 1 . a. . : X6 15.6 4.59 fn :-i.>X6A 18.3 5.39 V ^i^ X6i 21 6.19 1^ •■ :r^ X6 22.7 6.68 1 ■ :k>x6.^ 25.4 7 46 ]i- :H X6t 28 8.25 ..^..;i^ XG i x;t^,rX6A 29.3 8.63 31.9 9.4 iX^il X6i V x;^k X5 34.6 10.17 11.6 3.4 X.H,^,X5Js AX3i X5i 13.9 4.1 16.4 4.81 /'. S. S\ r. r'. r" C. 32 9.11 8.44 2.75 2.35 1.41 0.83 90000 8 10.95 9.83 3.27 2.35 1.43 .84 104800 36 12.87 11.22 3.81 2.36 1.44 .84 119700 64 12.59 11.52 3.91 2.28 1.37 .81 123200 86 14.42 12.82 4.43 2.28 1.39 .82 136700 I81I6.34 14.1 4.98 2.29 1.41 .84 150400 12 15.44 14.04 4.94 2.21 1.34 .81 149800 13 17.27 15.22 5.47 2.22 1.36 .82 162300 22 19.18 16.4 6.02 2.22 1.37 .83 174900 36 6.18 5.34 2 1.98 1.35 .75 57000 18 7.65 6.39 2.45 1.99 1.37 .76 68200 07 9.2 7.44 2.92 1.99 1.38 .77 79400 36 STRENGTH OF MATERIALS. Carnegie Steel Z Bars , — Continued Dlroenfdnos. w. o. J. /'. s. s\ r. t\ r'\ e. *X3i X5 ' 17.9 1.25 19.19 9.05 7.65* 3.02 1.91 1-31 .74 81000 AX3^X5A X3I X5i 20 2 5.94 21 «3 10.51 S,ft2 3.47 l,9i 1.33, .75 91900 22.0 6 64 24 53 12 00 9,67 3.94 1.02 1.35 .70 102100 X3>tX5ii^ 23.7 6.&ii 23 fiS 11.37 9.47 3.91 I.S4 1,23 ,73 lOlOOO 2Q 7 04 26 Ui 12 ft3 10 34 4 37 1.85 1.30 .75 110300 rX3l XSi |X3?ffX4 AX34 X4iV X3AX'H 2«,3 S.33 2R 70 14,30 U 2 4,S4 1,80 1,31 .79 110500 8,2 2,41 6.2S 4,S:i 3.14 1.44 1.62 1.33 .67 335Q0 10 3 3.03 7.94 5.40 3 91 1.84 1,02 1.34 .m 41700 12.4 ^.m 9 03 77 4 07 2.26 1.02 1.36 69 49B00 X3i A4t>t AX3>|X4i 13. S 4.05 9 06 73 4.83 2.37 1.55 1.20 .60 51500 15,8 4.CfJ Ills 7.90 5,5 2.77 1.55 l,3t' ,67 5S700 17. fl 5.27 13.74 9.20 0.18 3.10 1.55 1.33 .09 65900 iX3AX4 la 9 fi,55 12 11 H.73 6, 05 3. IS 1 48 1.25 66 04500 1X34 X4A 20.9 B. 14 13.52 0.95 6.65 3 58 1.48 K27 .67 70000 X3AX4* 23 (J 75 14,97 U 24 7.26 4 1.49 1,29 ,69, 77400 :X2jix3 0.7 :.97 2.87 2. SI ? 92 11 1.31 1.19 55' 20500 ^X2f X3A S.4 2,48 3 0-1 3.04 2.,^ 14 1.21 1.21 .56, 25400 X2HX3 9.7 2.Sn 3 K5 3.92 2.57 1.57 1.10 1.17 .55 27400 i^X2| X3i^ X2RX3 AX2* X3^. 11.4 3.3d 4 57 4.75 2,98 1.8H 1.17 1.19 .56 31800 12.5 3. on 4.59 4.85 3 06 1 99 1.12 1.15 .55 32600 14.2 4. IK 5.26 5.70 3,43 2,31 1.12 1.17 ,50 30000 1 REINFORCED CONCRETE CONSTRUCTION. A reinforced concrete construction is one where concrete and steel are used jointly, being proportioned to carry the strains of compression and tension respectively. Such constructions have all the advantages of a purely masonry construction along with the elasticity of one of steel. They are ^rmanent, proof against fire, rust, rot, acid, and gas and do not require attention, repair, or nainting. Moreover, the strength of concrete increases with age, and a safety factor of 4 at the time of completion of structure may easily amount to 6 or 7 after the lapse of a year or so. Advantages. Crushed stone, sand, and cement are procurable on short notice, while structural steel is often subject to long delays in deliv- ery. Concrete may be molded into any desired form, and masonry simu- lated. Defler'tion under safe load is practically nil. It being essential that a beam fail by the T^arting of the steel, after its elastic limit has been exceeded the stretch is such that a reinforced concrete beam should deflect several feet before failure. Design. The concrete should be reinforced in both vertical and hori- zontal nlanes, the vertical reinforcement being inclined at an angle of 46® to the horizontal and aoproximating thereby the line of principal teninle stress. The shear members should be rigidly connected to the horizontid reinforcing steel. Steel should be distributed proportionally to the stress existing at any point. The concrete should be composed of the best grade of Portland cement, sharo, clean sand a.od broken stone or gravel (to pass a 1-in. ring) in the proportions 1 : 2.5 : 5 for floor slabs and 12.4 for beams. Steel bars should be at least 0.75 in. from bottom of beam. The concrete should be thoroughly rammed into place and the centering left in position for at least IS days, and, if freezing has occurred, for such additional time as may be required for every indication of frost to vanish and for the con- crete to become thoroughly set. Formulas for Strength of Reinforced Concrete Beams and Col- umns. Let A = area of concrete in sq. in.; a = area of steel in sq. in.; 5 = width of beam in in.; c = distance from neutral axis to center of steel section in in.; d = distance from center of steel section to top of beam in in ;. e- distance from neutral axis to top of beam in in. ; fts = tensile strength of steel in lbs. per sq. in.; /«e = tensile strength of concrete; /er = compres- sive strength of concrete; A = depth of beam over all, m in.; <f — REINFORCED CONCRETE CONSTRUCTION. 37 distance from center of steel section to'top of floor slab in in.; 6' => width of floor slab in in.; < = thickness of floor slab in in. Then, distance from 15a + bd^ neutral axis to center of reinforcing steel section, C'^'^ri: — rsr-,. Bendiner dUa + £oa Moment, B|»= y-^ + cjafta+-^ — (If tensile strength of concrete is dis- regarded, omit /ta&c*-^3. For safe loading take ^ to i of above values. /!««» 64,000 lbs. per sq. in.; /tc = 200 lbs. per sq. in. m formula.) Safe load on columns (where length < 15 X least diam.) m lbs. = 350(^4 -Hi 6a). (The above abstracted from catalogue of the Trussed Concrete Steel Co., Detroit, and appUcable to system of construction devised by their engineer, Julius Bfn in inch-lbs. ="0.333/«6e2-f.ac^^^. To determine position of neutral axis: rr—V" percentage of metal to total sectional area of beam; -7-=a: — on n the part of beam in compression. Then, assuming the steel to be located at I depth of beam (from top), x ■= 20y (yi + A^-lj. In calculating beams with floor slabs united thereto, the beam and slab are considered as a T section. If the neutral axis falls in the slab the Bm formula above holds good. If, however, the neutral axis falls in the beam below the slab, Bm = ^«^'(3d'-c)-(fi-pW-6)(3d'-fi-20]. When fee" 500 lbs. and /««» 16,000 lbs. (Safe working stresses, Phila. Bureau of Bldg. Inspection). e=d'+2.6. o(for T section) — B,n + 16,000 (<i'—|^) approx. Shear: — Beams without vertical reinforcement fail by cracking. The unit shear at the plane of reinforcement, q, — -, where X^the vertical shear at the section under consideration, /—moment of inertia of section » ^(steel) 28,000,000 „« i? ^r ^- e^ r/j/ «\ and tn^TTT^ tt" - ^/^ ^»/v =°20. Fora T section, q=» IT -t-6 id'— — ). E (concrete) 1,400,000 V 3/ Columns: — Vertical rods are placed near the comers of columns and bound together by lacings of wire or metal straps. In order to have joint action of the steel and concrete their deformations must be equal. Then fie+E (concrete) =-/«-^J5 (steel), or, ft8=feeE (steel)-^J5 (concrete). If /« = 600 lbs. (safe stress). /»«= 10,000 lbs., which is lower than the safe unit stress on steel, but the proper value to employ when fee —500 lbs. For square columns longer than ten diameters, fee should be reduced by the following formula: F«j— /«+ (n- 0.0005 p), where F«= allowable unit stress, /«.— unit stress allowed in short columns, &'=side of column in in., and Z=length of column in in. (E.G. Perrot, E. R., 5-28-04). Edwin Thacher, C.E. (E. N., 2-12-03) takes E (steel) at 30,000,000 and E (concrete) for a 1 : 2 : 4 mixture, at 1,460,000 (30 days) and 2,580,000 (at end of six months); //« as the ultimate strength of steel +10%; fee at 2,400 (30 days) and 3,700 (six months). In designing he gives the con- crete a certam factor of safety at the end of one month and the steel the same factor of safety as the concrete at the end of six months (4 for static loads, — 6 to 8 for moving loads). Ultimate strength of steel taken at 60,000 lbs. , whence, fts = 66,000 lbs. per sq. in. He deduces the following formulas r """^ ^^^ '^*^^' "^"^ ^^ °'''*^* 30 days. 6 mos. Ultimate Bm in ft.-lbs. for beam 1 in wide =36.8^2 and 53.07rf2. o . c * I 147.2d2 .. 212.3rf« Weight in lbs. at center producmg first crack- — y — — T — • , ,. .1^ . J, J t^ 3,533d2 ,. 5,095d« Uniformly distributed load per sq. ft. — — j^ — — Z*~' where L— length of span in feet. 38 STRENGTH OP MATERIALS. The following formulas are those of A. L. Johnson. C.E.. of the St. Louis Expanded Metal Fireproofing Co., and are used m connection wi£h the Johnson corrugated bars Modulus of elasticity of steel in lbs. per sq. in., i?8» 29,000,000; elastic fimit of steel. F = 50.000 lbs. per sq. in. For average rock concrete (1 • 3 . 6, i^ee^^^ modulus of concrete in com- pression -3,000,000. /« = 2,000, /tc-200), e=0.331/i; o6 -s- » - 0.0U6466/i ; • ultimate Bm in inch-lbs. » 301. 3&^2< For special rock concrete (trap rock and certain western limestones, 12 5, J5c«= 2,400,000; /ce = 2,400; /« = 200), e-0.418A; afe-^»=0.0116A (or 1.1% of remforcement) ; ult. iS^ = 4596^2. For cmder concrete (1 2 5, £?« = 750.000. /e.^750, /^^SO). e»0.483A a6+«=0.0046A: ult. B,n = 161.26/i2 In the above, distance from top of beam to center of steel — 0.9A, a = area of steel section of one bar. and s-^^ spacing of bars in inches. Shear — Let Afi= moment of resistance m inch-lbs. at one foot from end of beam carrying ultimate load: i3»7= ultimate moment at center; i "-elongation per inch of steel at section one ft. from end : S == ultimate shear- ing strength in the concrete (=tof tdt. compressive strength). Then, Mi d — c: P«» total stress in metal in width 6, in lbs.=^«Aa5-(-«S, which g^ves the pull in the bars to be absorbed by M e shearing stress in the concrete over an area =125. For safety Pg should not exceed 665. When the beam is loaded at t^o points som^ distance apart (or when uniformly loaded and the shear exceeds above limits) bars of different lengths should be used, the ends being bent up at 45**, beginning at a distance of i to ^L from ends of beam. Summary of Beam Tests. From about 200 reported tests, T. L. Con- dron (W. Soc. of Engs.. 3-15-03) deduces ti:e following formrla Ult. Bm^ (in inch-lbs.) = (nP+j5)fccP, where n = 460 for highly elastic steel bars positively bonded to the concrete ( = 275 for plain bars of ordinary struc- tural steel); P=» percentage of reinforcement = (100 X bar section) -i-M; 5 and cl in in. For ordinary concrete (1 3 6) P may vary from 0.5 to 1.25, economy- lying between 0.7 and 0.9 For extra strong concrete (12 4) P may be increased to 1.25. Adhesion. (From Mass. Inst, of Technology Tests.) fru_^ ^* T>„_ Adhesion in lbs. per sq. in. of metal section per linear lype oi uar. .^^^j^ ^ imbedment. Ransome, ^ in. Average, 3000(±33% for max. or min. respectively) i.. .. 2050(±15% •• *• •• ** ** ^ Thacher, i " *• 2560(±12% " •' *' •* « •* •• 2275(±16.5% •• •• •• •• Johnson, } " ** 5550(±31.6% ' I *• •• 3500(±28.6% *• •• *• •• Plain round, f •• " 1375. ** square, I '* ** 1170. (Also for all rectangular secticms of same area.) Types of Bars. Johnson - square section with corrugations on sides which are at right angles to the length. Ransome: originally square sec- tion twisted about 20°. Thacher circular section deformed to elliotical sections at close longitudinal intervals; section practically uniform throughout length. Kahn smooth bars, the boundary line of whose cross-section is the same as that of a rectangular bar (126 wide X 6 thick) upon which is centrally suoerimposed a square (side = 46), whose diagonal coincides with center line of bar. ((Vomers of square are rounded.) These bars are placed flat in beams, the thin webs on each side of the middle rib being sheared at regular intervals and bent upwards at about 45° inclina- tion, thus forming substantially the tension members of a Pratt truss and providing vertical reinforcement. The webs are only partially s!icared from bar, one end being left uncut from rib by a length sufficient to provide a rigid attachment. REINPORCED CONCRETE CONSTRUCTION. In other systems than the Kahn vertical reinforcement is obtained by bending individual rods upward at proper intervals. In the OumminfEs ey^texn rectangular links of varying: widths and lengths made from plam rods are used, the ends of links bemg inclined upward to provide for the vertical reinforcement. Stress Diagrams in Framed Structures. If three oblique forces maintain a body in a state of rest, their directions meet at one pomt and their proportional values may be shown by the respective sides of a tri- angle drawn parallel to the forces. U a body remains at rest under the action of a number of forces in the same plane, their relative magnitude may be shown by a polygon whose sides, taken in order, are drawn parallel to the forces. II. m. Piff. 6. Ctoneral Case* Simple Roof Truss (Fig. 6). i weight of a6(TF) will be supported at each pohit, a and &• i •• *' adW) *• •• *• •• •• •• a •• & The weight, then, at a— 2 ' The reaotioo at B which balances a— ^^K , * Z I B' •• •• a Total xeaction at B -^ + ^"tEl J 2 2 40 STRENGTH OF MATERIALS. The forces being thus stated, letter each cell or enclosed space (in this case but one, i.e., the triangle A), and also each section of the external space as divided by the lines of the forces and the members of the truss. ^ ¥ K v\ ^ /\ ^ /o\/ e\/ A 6 /\H c\/a\ J ^ K 1 L \ M I T 1 ^ w Fig. 7. A A \ p / / \ h M \ fA' A B \ \ / \i / 0. r K (5)1 ■« m M A%\%VA%\ X S^j 1 M : i FS«.ia. O.BW W W IRT O.^W 1 K I L I M I N 1 ftg.9. as B, C D, ^, and F. Draw the force diagram for each set of radiating forces. Consider the four forces at the point c, each defined by the spacisU letters thus: FB^ BC^ CA^ AF (using one direction of rotation through- STRESS DIAOBAHS. 41 out, — ^preferably right-handed). Set ofiF in the force diagram FB^ W and BC^R' = — + — — T— . Draw AF parallel to the right member of truss, ac' then AC will be parallel to he and meet EC at x>oint C (see I). Notice that arrows must follow each other around the diagram in one direction. II and III show direction of forces for points a and &. AF, Fte.io. AC^ and AE in the force diagram are then the stresses in the members of the truss and are measurable by the scale assumed for W and W. Place arrows on the members of the truss as indicated by I, 11^ and III; then, arrows pointing toward each other show that the member is in tension and vice versa for compression. Generally AE=^AF, W = W', and R'^R'^W: The truss diagrams (l*igs. 7, 8, 9, and 10) illustrate the application of the preceding principles. Redundant members (those not stressed ex- cepting when distortion takes place) ma^ be determined by inspection and their number » the number of members in excess of [(twice the number of joint*)— 31. r 42 STRENGTH OP MATERIALS. Fi^. 7 shows the stresses in a symmetrically loaded Waxren trufli, Ltf,, by the weiffht of its members. Fig. 8 shows the same truss under aay coacen- trated load W, which may be taken for a rullins load by determining the stresses caused at each joint by imposing this load, ami designing each member for the maximum stress it may have to withstand Note from BC, CD (Fig 8), as compared with same member* in Fig. 7, that the mem- bers are subject to either tensile or compressive stress and should be cal- culated for the greatest stress of each kind. In the rafters of the roof -truss (Fig. 10) the load on each rafter=>Tr, and, having three supports, is divided (as per table for Continuous Beams, ar\i^ as follows: -r^ at each end support and —r^ on the middle support. lo Id The total horizontal ^ind pressure, Prf = 40 to CO lbs. per sq. ft. X width of bay between two rafters X A; (see diagram)] is resolved into two compo- nentr, — one parallel, and one normal to the rafter. The latter, Pn——^ ac and is distributed at a, d, and c as '-r~, —5—, and -rs-t respectively. lo o lo If a be fixed and b loose, expansion is provided for, and the reaction R' is vertical. R, R\ and Pn mutually balance and meet in the point x (foimd by producing Pn to intersect R'). By connecting 12 and x the direction of R is given and values of R and R' are obtained from the auxil- iary force diagram. If the wind blows from the right, Pn acts on he, and z will be above instead of below 6. Each member should be designed to resist the maximiun stresses in it caused by the weight of roof, rafters, snow, and also the wind pressure, from whichever side a maximum stress in the particular member is caused. Framed Structures of Three Dimensions must be solved by con- sidering each plane of action separately. For example, in a shear less substitute for the two rigidly attached legs a single one in a plane with the third or jointed leg, determine the respective stresses, and then resolve the stress in the substituted leg into the stresses for the two legs it replaoeai ENERGY AND THE TRANSMISSION OF POWER. Force and Mass. The tmit of force in engineering is one pound avoir, dupois. Mass, or the quantity of matter contained in a body, — — ??-.• i; = 32.16954(l -0.00284 cos 20 ( 1 -— ) , where r = 20,887,510(1 + 0.00164 cos 20, [in which Z- latitude in degrees, fc = height above sea-level in feet, and r = radius of the earth in feet. In calculations g is ordinarily taken as 32.16 in the U. S. Velocity» or the rate of motion, is estimated in feet per second. If uni- form, 9=^—, If imiformly varying from V\ at beginning, to V2 at the end of the time /. a^^^^t . (1). Acceleration (/) is the increase of velocity during each second, and, if uniform, is produced by any constant force, the force being measured by the increase of momentum it produces. Momentum, or the quantity of motion in a body— mass X <relocity=mt;, and force producing acceleration '^wf-hg. /=^^^^ (2). Combining (1) and (2), »=-»,<+-|^ (3). Ifvi-O (starting from a position of rest), »— "o" ("*) *°d ^^~t' ^^^' Substituting (5) in (4), v^=2f8 (6). For retarded motion (3) would read: »=t;i«— ^. Impact of Inelastic Bodies. Two inelastic bodies after collision will move as one mass with a common velocity, and the momentum of their combined mass is equal to the sum of the momenta before impact. (mi+m2)i>(final)-="mit;i+m2V2. v^— — . ^"^ accordingly as the bodies m\ + wia move in the same or in opposite directions before collision. The Pendulum. A simple pendulum is a material point acted upon by the force of gravity and suspended from a fixed point by a line having no weight. A compound pendulum is a body of sensible magnitude sus- pended from a fixed point hyaline or rod whose weight must be considered. The center of oscillation is a point at which, if all the weight of a compound Eendulum be considered to be there concentrated, the oscillations will ave the same periodicity as a simple pendulum. The distance of the center of oscillation from the point of suspension = (radius of gyration )2-h distanoe of center of gravity from point of suspension (o). An ordinary pendulum oscillates in equal times (isochronism) when the angle of oscil- lation does not exceed 5°. Let Z— distance in in. between point of suspension and center of oscilla- tion of a simple pendulum, < — time in seconds for n oscillations, and n = number of single oscillations (one side to the other) in time U Tnen, for a flunple pendulum, l"-;;^ = -^^. 43 44 ENERGY AND THE TRANSMISSION OP POWER. 4a r* For a compound pendulum (rod of radius r) : ^ "" "o" + ^ I (baU of radiua r): ^-o + ^. ball of weight W (dist. o) and ball of TT, v'dist. oi), both on same side of point of suspension; Z= — ~^ ^ w^ ' Balls W(a) and Wi(ai), point of suspension between: dist. of c. of g. of system. x= ^^.^^ . and Z- --^^- ^^ . In the last two cases W is the larger wei£[ht, and the weight of connecting line or rod is neglected. The length of a sample pendulum which oscillates seconds at New York is 39.1017 in. Energry. or the capacity for performing work, is of two forms: Potential Energy, which is stored or latent, and Kinetic Energy, or the energy of motion. In any system, kinetic energy + potential energy >= a constant. In any machine the eneigy put in = the useful work given out + the work lost by resistances. (Stored energy not considered.) Either kind of energy may be transformed into the other kind. Estimate of Energies* The Potential Energy^ of a weight w, at height H^wH ft.-lbs. If allowed to fall, the velocity on reaching the ground, v = v^S/T, from (6). But / - ^, and » = H. .*.«-= >/^ff and ^ =■ ^. Substituting (in wH), Energy (now Kinetic) in ft.-lbs. = -jr- , which is ap- ^0 plicable to all cases of moving bodies, it being strictly proper to assume that the velocity is caused by gravity. When a body rotates around an axis (e.g., rim of fly-wheel, of weight, to), V (Unear) — 2KRn, (n -» ^) and the Energy of Rotation in ft.-lbs. — -g— = 1^^.0.0001704«,«W. The Energy of a Compressed Springs— ft.-lbs.; the Energy of a Compressed Gas = mean effective total pressure X stroke. The Energy of One Heat Unit (1 B.T.U.-=1 lb. water raised 1° F. when near 39^) =778 ft.-lbs. Energy of Power Hanuners. Energy of falling hanmier»— . En- ergy received by the hot iron*- mean total pressure in lbs. p, Xaepth of impression H, in feet, and pH^-^r-. .*. p=»ir-fr« The greatest total £g jigJti pressure = 2p. Energy of BecoU. Let i&i and tco^weifrhts of gun (with carriage) and projectile; vi and «2= velocity of recoil and projectile velocity at muzzle. Then , wiVi «■ W2V2 and vi ■= — ^ The energy of a body in motion = Wi -^r— , hence the energy of recoil = «;i(—^) +2g, and the energy of the ^g \ W\ ' projectile = \d^i>^ -*- 2g. Power is the rate at which work is performed, the, unit being one horse- power, or 33,000 foot-pounds exerted during one minute. Elements of Machines. A machine is an assemblage of parts whose relative motions are fully constrained, dnd its purpose is the transmission or the modification of power. Let P be the point where the power is applied and W the point where it is removed or utiUzed. Then, work put in at P==work taken out at W (neglecting resistances). As work= force X distance , P« = W%\ , or -p «= — , where » and «i are the distances traveled by P and W. Further, velocity of P force ^ w u • 1 a j * ^ — i — - J r nr ^i „= Mechanic al Advantage, ^. velocity of W force P -• » p ELEMENTS OF MACHINES. 46 The liever. By the prinoiple of moments, Pr—Wri and the Mechanical Advantage — q- « — , r and ri being the respective radii of " ri P and W from the fulcrimi (for straight lever and parallel forces). Iiever Safety- Valve, Let w, wi, and W be the weights of lever, valve, and ball, respectively in lbs., r, ri, and R the distances from center of gravity of lever, valve center, and ball center to fulcrum, in in., d the valve diam., in in., and p the steam pressure per sq. in. of valve. Then, ^ (0.7854pd2-tt>i)n-tor ^ R • If the lever is bent or the forces are not parallel, the arms fi and R are then equal to the length of the perpendicular drawn from fulcrum to the line of direction of each force. Wheel and Axle. Mechanical Advantage ""-5— — z -j-. — ; K axle radius Train of Gearing. P is applied at radius of first wheel, transmitted by its toothed axle to circumference of second wheel which is toothed, by second axle circumference to third wheel circumference, etc. Mechanical Advantage , p " p" ^ ;^ X "^ » ®*® • Block and Tackle. The pull P on the rope through the distance s will raise the weight W through the distance »i- No. of plies of rope shortened by the pull* __,.,-, . W No. of plies shortened , , , Mechanical Advantage —p— ^ . In any movable W 2 pulley, p — y, TT rising only one-half the height that P dbes. Differential Pulley. Two pulle3rs whose diameters are d and di rotate as one piece about a fixed axis. An endless chain passes around both pullesrs and one of the depending loops of the chain passes around and supports a running block from which W is hung. P is applied on the cham running directly to pulley of larger diam., d. -,..,.. ^ W P'sdist. nd 2d Mechanical Advantage=p -_^^-^^^-.^-^. 2 Inclined Plane and Wedge. While P moves through base 6, TT is raised through the height h, and Mech. Adv. ==-5^ =»-^. A cam is a revolving inclined plane. The Screw is an inclined plane wrapped around a cylinder so that the height of the plane is parallel to the axis of cylinder. It is operated by a force applied at the end of a lever-arm (of length r) perpendicular to axis. Let p" = pitch of screw = height of inclined plane for one revolu- - _,,„,. J IT P's dist. 2itr tion of screw. Then, Mech. Adv. =° -p- = „., .. . '^-jt' P H^'sdist. p" Connecting-Bods are subject to alternate tension and compression and the diam. di at mid-length is calculated by means of Gordon's formula for colunmd (both ends hinged) where r^ = di^-i-16, using a safety factor of 10 and values of a and 6 for steel. The diam. at small end (d) is designed to resist compression only, that at large end (dj) being obtained by con- tinuing the taper from small diam. to diam. at mid-length uid thence to the large end, and is equal to 2di—d. Kent gives as the average of a large numb er of f ormulas considered by him: di » 0.021 X diam. of cylinder X V^p (steam). Ba rr gives as the average of twelve Am. builders di = 0.092V^cyl. diam. X stroke (for low-speed engin es), and thickness, (for rectangular sections, high-spteed engines) =» 0.067 v^diam. cyl. X stroke breadth => 2.7^ All dimensions in inches. M, t 11 46 ENERGY AND THE TRANSMISSION OF POWER. Oonnecting-Bod Ends. Strap-end: width =» 0.8m, thickness = 0.22m (increased to 0.33m at mid-length and also at ends when slotted for gibs and cotter); depth of butt-end of rod=»l.ldl+Ain. cl**-diam. of crank-pin, m = d+0.2 in. Crank-Arms (Wrought Iron). Hub diam.^l.Sd; hub length = O.Sd; diam. of crank-pin eye = 2di; length of eye = 1.4di; width of web = 0.76 X diam. of adjacent hub or eye; thickness of web »0.6X length of adjacent hub or eye ((f» least diam. of shaft; di^diam. of crank-pin). Valye^tenu. Diam.. ^..^/tota l prewure^vijve £ ^ Eccentrics. Sheave diam. = (2.4 X throw) :f ( 1 .2 X shaft diam.) ; breadth — <fs+0.6 in.; thickness of straps 0.4^8 +0.6 in. (ds="diam. of valve- stem.) SHAFTING. For strength against permanent deformation, d""3.33y--^. For stiffness to resist torsion (max. allowable twist < O.OVd** per foot in length), */W¥ d-4.7r -if^. These values are for W.I.; for steel shafts d has but 84% N of the values given by formulas. In designing take the larger of the two values of d obtained from th e formu las. Average Practice. d'^V ' ^^ ' , where c (for cold-rolled shafting) for shafts carrying pulleys ="75; for line shafting, hangers 8 ft. apart, « 55; for transmission only, =35. For turned iron shafting under similar con- ditions multiply value of c by 1.75. Length between bearings to Umit de flection to 0.01 in. per foot of shaft- ing: f or bar e shafts, L (in feet) = i{/720d*; for shafts carrying pulleys, L-^140d2. Fly-wheel Shafts. For shafts canying fly-wheels, armatures or other heavy rotating masses, find the eauivalent twisting moment of the combined torsion and bending in inch-los. and apply same in the two formulas at the beginning of this topic, remembering that Twisting moment-^^^ . ^-63,025 ~^. (See p. 31.) S /XT -p Average Engine Practice. Crank-shaft diam.. d= 6.8 to 7.3 X T -j^ for low and high speed respectively (Barr). Also, d=0.42 to 0.5 X piston diam. (Stan wood). N for machine-shops = 120 to 180 ; for wood-worldng shops, 250 to 300; for cotton and woolen mills', 300 to 400. JOURNALS. The allowable pressure p in lbs. per sq. in. on the projected area (IXd) of journals is as follows: For very slow-speed journals, p= 3,000; for cross-head journals, p = 1,200 to 1,600; for crank-pin journals, low speed, p— 800 to 900; ditto. Am. practice, 1,0(X) to 1,200; for marine engine crank-pin journals, 400 to 500; railway journals, 300; crank-pin journals for small engines, 150 to 200; main bearings of engine, 150; marine slide- blocks, 100; cross-head surfaces, 35 to 40 lbs. per sq. in.; propeller thrust- bearings, 50 to 70; main shafting in cast-iron boxes, 15. Overhung Journals. On end of shaft. Constant. pressure. When JV<150, d=-0.03V^for W. I., and 0.027>/P for steel; -^ = 1.5 to 2. When a N>150, d=0.0244V|JPTd for W.I. and O.OlWlp^d for steel. Also ■j-0.13v^ for W.I. ©nd 0.17v^iV for steel. BALL AND ROLLER BEARINGS. 47 Journals under Alternating Pressures (e.g., crank-pin). When N<150, d='0.027^/P for W. I. and 0.024VT for steel; ^^1 for W. I. a and 1.3 for steel. When N> 150, rf-0.0273r^ for W. I. and 0.02r~ for steel; -^=0.08>/F for W. I. and O.iv^ for steel. Am. Engine Prac- a tice: d(for crank-pin) =0.22 to 0.27Xpi8tpn diam.; 2=0.25 to O.SXpis- ton diam. (Stan wood). Ooss-head pins: di = 0.8d; /i==1.4di. Neck Journals, or those formed on the body of shaft need but two- thirds the diameter of overhung journals of the same length. For ball and socket shaft-hangers, 1 = 44', depth of shoulder on neck journal may be taken as 0.07d+i in. Pivots. For iV<150, p = 700, 350, or 1,422 lbs. per sq. in., and d=VpX0.05, 0.07, or 0.035, for W.I., on bronze, C.I. on bronze, and W.I. or steel on lignum-vitae, respectively. For iV^> 150, d = 0.004VpiV and 0.035 v^ for W.I. (or steel) on bronz e and lignum- vitae, resp ectively. Collar Bearings. Outside diam. i>-l/d2+*2^l!lIH^i^lbs. ^j^^^_ 47Xno. of collars ness of collar=0.4(D— d)= ^Xspace between collars. (d = shaft diam.). Shaft Couplings. For a cast-iron keyed sleeve-coupling, /»2.66d + 2 in.; external diam. of sleeve = 1.66d+ 0.5 in. For a cast flange coupling, I of hub on each half =1.33<i+l in.; hub diam. = 1.66d+ 0.5 in.; flange diam. = 2.5d+4 in.; flange thickness =0.166d+0.42 in.; width of flange rim=0.35d+0.86 in.; no. of bolts =« 2 + 0.8rf ; diam. of bolts— g^+A in. For plates forged on abutting shaft ends, t^O.Sd; outside diam.— 1.W+ (2.25 X bolt diam.); no. of bolts=-|. (d=shaft diam.) Brasses should have a thickness in the center (where wear is greatest) -0.16d+0.26in. BALL AND BOLLEB BEABINGS. Boiler Bearings. Let n= number of rollers; <2=diam. of rollers in in. (for conical rollers take diam. at mid-length); i = length of rollers in in.; then, if the rollers are sufficiently hard and are so disposed that the load is equally distributed over I and n, Load in lbs. P=cnld, where c==356 for C. I. rollers on flat C. I. plates, and 850 for steel rollers on flat steel plates (Ing. Taschenbuch). Friction may be reduced 40 to 50% by the use of roller bearings. The Hyatt flexible rollers consist of flat strips of springy steel wound spirally into tubular form; they give at all times a contact along their entire lengtl^ It is claimed for them that they save 75% of the lubrica- tion (and 10 to 25% of the power) needed by ordinary bearings of equal capacity, and that they cannot become overheated. Ball Bearings. Diam. of enclosin g circle = (d + c)F + d, where d = diam. of ball; c= clearance between each pair of balls; F, a factor as follows: No. of balls 14 15 16 17 18 19 Factor/^ 4.494 4.8097 5.1259 5.4423 6.7588 6.0756 No. of balls 20 21 22 23 24 Factor P 6.3925 6.7095 7.0266 7.3338 7.6613 d+c or, generally^ D=d-\ r^^, where n=no. of balls. sin n If 0.005n>— , take c^— ; otherwise, c= 0.005. All dimensions in 4 n inches. BaUon Between Flat Auto Machy. BaU. Plates. Co. 1280 1814 1288 4153 6570 5150 9030 12700 11600 16710 22610 20600 28680 30000 32260 59030 90650 82400 48 ENERGY AND THE TRANSMISSION OF POWER. Crashing Strength of Balls. Breaking Load in Lbs. ' Safe Load. 160 640 1450 2670 4030 10300 - The Auto Machinery Co.'s data answer to breaking load — 82,400d2 and are a fair average of the first two columns (results obtained by F. J. Harris at Rose Polytechnic Institute), the surface of ball race being con- sidered as between a spherical and a plane surface. Greatest load on a single ball «= r^ ^ , „ in an annular bearing where n ranges from 10 to 18 (Stribeck, Ing. Taschenbuch). Prof. C. H. Benjamin recommends a safety factor of 10, that in above table is 8. Radial Ball Bearing, with 4 point contact, ^fgafe)'^(^)^^ If P> 3,000 lbs.. P-300+290rui. ^ ^ Thrust Bearing, with 3 point contact, ^(safe)^^'^'^ ^ ^'^^ Ibe.) » l,143(nd-2i); P(safe)(4.500 to 8,600 lbs.) = 2,125(nd-4); ^(safe)^^'^^^ to 17,000 lbs.) = l,500+808nd. Thrust Bearing, Balls between Flat Plates. Whennd -35 7 9 10 P, safe, in lbs. = 475 1,200 2,200 3,200 5,000 Thrust Bearing, 2 Point (Balls in Races of Larger Diam.). When nd = 3 6 8 10 12 14 P, safe, in lbs. = 300 800 1,500 2,750 4,000 4.809 Belation between Ball Diam. (d) and Shaft Diam. (D). Three-point Thrust Bearing, d = 0.143+0.17I> Flat-plate " " d = 0.125-l-0.19D Two-point race * ' * * rf = 0.0625 + 0.166D Radial, four-point * * d - 0.3I>, when D^ 1 .6 in. *• d=0.3H-0.15Z>when2)>1.5£n. The foregoing proportion represents the practice of the American Ball Co., of Providence, as derived from their catalogue by the author and may be taken as guidance in design. Friction of Ball Bearings.. M. I. Golden (Trans. A. S. M. E.) from experiments on balls from i to ^ in. in diam. m radial or annular bear ings at speeds from 200 to 2,000 r.p.m., deduces as a tentative formula' Friction = Load (o.005 + ^*^* -H0.005I>), where d=diam. of ball, and Z><»diam. of path of balls in the races. At speeds aroimd and exceeding 2,000 r.p.m. chattering takes place, which may be reduced to a marked degree by the use of oil. He Found /x = 00475 (taken as 0.005 in formula). Double Ball Bearings. In an ordinary ball bearing the turning of the shaft rotates the balls in such a manner that the surfaces of two con- tiguous balls rub or grind upon each other, and this is said to be the cause of a large proportion of the failures recorded in the use of ball bearings. In the Chapman double ball bearing a smaller ball (not in contact with the shaft) is introduced between every two balls of the bearing proper, and a rolling contact throughout the bearing is thereby estabUshed. The Chapman Co. (Toronto, Ont.) claim to save 80% of the work lost in fric- tion by ordinary self-oiling journal bearings, and refer to runs of 1^^ to 2 years duration without lubrication or appreciable wear. QEAHING. 49 GEARING. Spiur Gears are toothed wheels for transmitting power between parallel shafts, the teeth being parallel to the axes of the wheels. They are equiv- alent to friction cylinders or discs having teeth provided to avoid slipping with heavy loads and, with an infinite number of teeth, the gears .would become smooth-surfaced cylinders engaging with each other at their cir- cumferences. These circumferences are called i)itch circles and the velocity relation between any two wheels is determined from their respec- tive pitch circle radii For trsmsmitting perfectly uniform motion the curves of the teeth are specially formed, the condition for such motion being that the normal to all surfaces of contact between the teeth must pass through the meeting- point of the two tansential pitch circles. Eplcycloidal Teetn for wheels are formed as foUows: The part of tooth curve outside of the pitch circle is the path of a point on the cir- cumference of an arbitrarily chosen circle which rolls on the outside of the pitch circle, and the part of tooth curve inside the pitch circle is the path of a point on the circumference of the same arbitrarily chosen circle when rolling inside the pitch circle. For racks the pitch circle (of infinite diam.) becomes a straight line and the tooth outlines are generated bv a point in the circumference of a circle roUing on the line above and below Where gears are to work interchangeably the same rolling circle must be used throughout Teeth should be designed so that at least two pairs are constantly engaged Involute Teeth possess an advantage over epicycloidal teeth in that the distance between the wheel centers may be slightly varied without affecting the accuracy of contact; they are generated as follows: Draw pitch circles and connect their centers. Through point of ccmtact ot circles draw a line inclined at an angle of 75° to the line of centers and from each center draw a circle tangent to this line. These circles are base circles and the tooth curve in each wheel is the path made by a point in a line unwrapped from the base circle of that wheel. The prolonga- tion of the outline inside the base circle to depth of tooth is a radial line. Diam. of base circle =» 0.966 X diam. of pitch circle. Involute rack teeth have straight outlines which make an angle of 75** with the pitch line. Circular Pitch (p") is the distance on the pitch line between the centers . ^ . . .t ,, ?rXdiam. of pitch circle of two successive teeth. p"=» rr . ^ ■ . '^ No. of teeth IHmnetral Pitch (pd"), or the number of teeth per inch diameter of •X V • 1 No. of teeth ir tt j i i • x pitch circle ^^r^ ch^Ur-^kdb- Used largely m cut gearing. Proportions of Teeth. If diam. of rolling circle for generating epi- cycloidal teeth is taken equal to 1 .75 X circular pitch, the tooth outline from pitch circle to bottom of tooth in a pinion of 11 teeth will be a radial line. Addendum (or radial height of tooth outside pitch circle) = 0.3/>"; Dedendum (or radial depth of tooth inside pitch circle) =0.4p"; hence, 19 total length of tooth = 0.7p". Thickness of tooth on pitch circle — r^p"; space between teeth = 2qP" ; back-lash = — ^— p" = ^ ; clearance = (0.4— 0.3)p"-jQ. The foregoing for cast wheels. For cut gears sub- stitute 0.3, 0.35, 0.65, 0.485, 0.515, 0.03, and 0.05, respectively, for the above coefficients of p" (Sellers). Diametral Pitch Formulas for Small Gears (Brown & Sharpe Mfg. Co.). Let P = diametral pitch; ZV, 4' = pitch circle diameters; D, rf= outside diameters; N, n = nos. of teeth; V, r«= velocity ratios (capitals for gear and small letters for pinion engaging with same); a = dis- tance between centers of wheels; 6 = no. of teeth in both wheels. Then, NV PD'V r>_ 2a(JV+2) . , 2a(n + 2) ^ 2av ^, 2aV 50 ENERGY AND THE TRANSMISSION OP POWER. For a single wheel (in addition to foregoing lettering), let <» thickness of tooth or cutter on pitch circle; !)"=• working depth of tooth; » = adden- dum; /—amount adcled to tooth depth for clearance; />"+/*- total depth of tooth; i>'-=circular pitch. Then. ^-=^^^*^-p-. ^^yi D-^^-Z)'+^; D"-^=2«; iV^-Pi>'-PZ)-2; '-10' *- P ~T* • P K -0-31»3P'-j^ "jNr+2' •+'"pV^+ 20/ =0.3685P'. Bevel Gearlns is used to connect shafts whose directions meet at any angle. The pitch surface of each gear is the frustum of a cone, both cones having a common vertex. The teeth have their surfaces generated by the motion of a straight line traversing the vertex while a point in the line is carried round tne traces of the teeth on a conical surface, which surface is generated by a line drawn from the extremity of larger diameter of pitch surface frustum to the axis and perpendicular to an element in the pitch surface. Spiral Gears are used to connect non-parallel shafts which do not intersect. Let a »» angle of inclination of axes, and Tt v, n, R, N, t, and T be respectively the pitch angle, circumf. velocity^, revolutions, radius* no. of teeth, circumferential pitch, and normal pitch of wheel A^ and n* vi, ni, etc., similar values for wheel B. rru . . lono J ^ s in r u »*i i? sin r N Then, r+n+a = 180** and — = -. — ^, whence — —is — : — — ^TF- ' ' © sm n n Ai sm n -^i r— / sin r and Ti^/i sin n* and as T must equal Tu t '=^?-^. For mini- Ci sm r mum sliding make r^'n- The position of the common tangent at point of contact of the pitch cylinders is determined from -js- *■ ^^— ^ •= ( — + coe a) JKi cot n ^ « ' •*■( — hcosoV Also, cotr = ~ — • \ni / • ' n . — hcosa ni T? nno **i X revs, (n) of follower ^ For «— 90**, — =cotrt or, \ \ . , . ^ »tan r* n revs, (ni) of dnver ' Worm Gearing. In this case a»90°, JV«1 and the teeth of B are inclined at an angle r to the edge of wheel, and tan r^^o^R"^'^^®^^* Strengrth of Gear Teeth (Wilfred Lewis). Load in lbs. transmitted by teeth, W=fp"by, where 6= width of tooth face, and t/=a factor depend- ing on the no. of teeth (n) and the curve employed. . y. for m volute teeth. 20** obliquity =0.164-^^^^^; n •• 15** •• (and epicycloidal) -0.124-^=^; n * • • * teeth with radial flanks = 0.075 - ^^. n Safe Working Stress, f. In lbs. per sq. In. Speed of teeth in feet per min. 100 250 500 1,000 1,500 2,000 2,600 Steel, /= 20,000 14,000 11,000 7,600 6.200 5,400 4^00 Bronae, /= 15,000 10,500 8,200 5,700 4,600 4,000 3.600 Cast Iron, /= 8,000 5,600 4,400 3,000 2,500 2,200 1.900 Approximate Strength. Safe load W, in lbs.=3006p" for C. I. (1206p", if shock is to be provided for. Lineham). Bawhide. W in lbs. = 57 to 114X6p" (Ing. Taschenbuch). An American gear-maker, however, states that rawhide has the same strength as cast iron. Bevel Wheeto. W-W'byx^!^^ ^'^- °f frf^^ . large diam. of bevel BELTING. 51 H^. Transmitted »(Trx velocity of teeth in feet per inin.)-»- 33.000. Safe Maximum Speeds. 1,800 ft. per min. for teeth in rough, cast (iron) wheels; 2.600 ft. for cast-steel and 3,000 ft. for machine-cut caat- iron wheels. Proportions of Gears. Face, 6 = 2p" to 2.5p"; thickness of rim* 0.4p"+ 0.125 in. at edge (add 26% for center); thickness of rim on bevel wheel (larger end) = 0.48p" +0.16 in. (taper to vertex); width of oval arms (in plane of wheel) =-2p" to 2.6p"; thickness ot oval arms (par- allel t o shaft) = p^^ to l.25 p". or half the width of arm; No. of arms» 0.55 VNo. of teeth X^^p^; taper of oval arms: — 2p" to 2.5p" wide at hub end tapered to from 1.33p" to 1.66p" at rim; thickness of hub = p"+0.4 in.; length of hub^b to 1.256. For arms of cruciform section: width of webs in plane of wheel =2p" to 2.5p"; width of webs in plane of shaft » 6 to 6 + 0.08p"; thickness of webs in plane of wheel —0.036p" (No. teeth -s- No. arms); .thickness of webs in plane of shaft =0.32p"+ 0.1 m. Drivlns Chain. Allowable velocities -600 to 600 ft. per min. No. of teeth in sprockets - 8 to 80. Radius of sprocket = p" + 2 sin (180* •*- No. of teeth)* p"-= length of chord bet. centers of two adjacent teeth. The Benold Silent Chain Gear consists of a chain made of stamped links of a pecuUar form which runs on an accurately cut sprocket wheel. These links are joined by hardened-steel shouldered pins and are pro- vided with removable split bushings. Advantages: high speeds (up to 2,000 ft. per min.); largest size (2 in. pitch, 10 in. wide) transmits 126 H.P. at 1,000 ft. per min.; positive velocity ratio; can be used on short centers, in damp or hot places, runs slack, thus obviating excessive journal fric- tion ; the contact is rolling instead of sliding and the running is practically noiseless. No. of teeth, 18 to 120. Where load or power is pulsating, a spring center sprocket is used to absorb the shock. BELTING. On account of slip, belting does not transmit power at an exact velocity ratio, but it is nearly noiseless and can be used over distances not exceed- ing 30 ft- without intermediate support. Belt Tension. In any belt strained around a pulley and in motion there will be a slack side and a tight side. The tension on the tight side is equal to the tension on the slack side plus the frictional resistance to the slipping of the belt on the pulley. The relation between Tn (greater tension) and U (lesser tension) is: Log (Tn -i-tn) =0.4343/iZ-i-r= 0.007678 a*^, where /+r = (arc of pulley embraced by belt)-*- (radius of pulley), and 0° = degs. of arc of pulley embraced by belt. fit (coefficient of friction) for leather belts on iron pulleys = if dry, and 0.16 if oily; for wire rope, a£ = 0.16 on iron pulleys and 0.25 on leather-bottomed pulleys; for hemp rope on iron pulleys, /<— 0.18 to 0.28. The Driving Pull of a Belt^Tn-tn, and the Ho^e-Powe, Tr.n^n.iHe<i.Q^)v . ^^"-^^'^ . Streng^th of Leather Belting, ft (safe) =320 lbs. per sq. in. of sec- tion, which allows for lacing or other jointing (or, 276 lbs. for laced and 400 lbs. for lapped and riveted joints). Single belts run from A in. to A in. in thickness; double belts from f in. to i in. Section must be suf- ficient to meet Tn. Rubber belts: /( = 11 Ihs. X No. of plies X width in in. Tension in Belts due to Centrifugal Force (unimportant at low speeds). fi = (where ti7 = weight of 1 cu. in. of leather = 0.0368 lb.) — 0.0134t>2, and total tension on tight side = rn + 0.0 1346<v2, Creep, Slip, and Speed. As the belt tension changes from Tn to tn a slight retrograde movement, or creep, occurs which is due to the release of tension and which causes the f<)nf)wer pulley to revolve at a correspond- ingly decrea.sed rate. This result is called the slip, and the loss amounts to about two per cent. Belt Speed. Generally not in excess of 4,000 ft. per min., at which speed max. economy is shown. Belt speeds however rise as high as 6,000 ft. per min. 52 ENERGY AND THE TRANc^MISSION OF POWER H. P. of Belting (approximate formula). „„ belt width in m.X pulley diam. in in. X revs, per min. - . , H.P. 2300 ^'''' °^«^ belts. For double belts divide by 1,960 instead of 2,800. Sag of Belts and Proper Distance between Shafts. (Sa« in in.-><; Length in feet =L.) Narrow belts over small pulleys, L-=15 ft., « = 1.5 to 2 in.: wider belts over larger pulleys, L = 20 to 25 ft., a '^2.5 to 4 in.; main belts over very large pulleys, L — 25 to 30 ft., a = 4 to 5 in. Length of Belts. Open belt: L^«(R-^Ri)-\-20(R-Ri) + 2lco8 fi; Crossed belt : L = 2(ft + fti) (-|- + ;?) + 2i cos ;9 ; where L - length of belt in in., A and iJi = radii of larger and smaller pulleys, respectively, j9«= angle between straight part of belt and center line of pulleys (*»No. of degrees Xw -5-180, in circular measure), /= distance between centers of pmleys in in. Cone Pulleys (open belts). The length of belt must be the same for each pair of pulleys in the set, and the radii of the pulleys have the following relation: RRi-(1.01^14l+c)Ri.-(1.004724l+c)R=0.51657P- (1.01414i-f-c)(1.004724Z-l-c). I being fixed by the design, insert values of R and Ri for any one pair of pulleys and solve equation for c. Let the ratio of R-^Ri for any other pair of pulleys = n. Substitute ni2i for R, also value of c in equation and solve for Ai, taking the negative value of the root of right-hand member of the equation. This formula is absolutely accurate where /SOO*', — a limit including all practical applica- tions. (For derivation see article by the compiler in Am. Mach., 5-19-04.) Let n and ni be the lowest and highest respective speeds for any set >of cone pulleys, and x the number of speed changes; then, the speed ratio between any two successive speeds, a—. «/ — , (geometric ratio). If a back-gear is used the number of speed changes is doubled and the speed ratio of the back-gear corresponds to the term of the series where it is introduced. Principle in Belt Driving. The advancing side of belt must move at right angles toward the shaft it approaches, while the retreating side may make any deviation. Lacing. Punch 6-1-1 holes in each end of belt, arranged sigzajg in two rows. The edges of holes should be i in. from sides and f in. from ends, — rows at least 1 in. apart. Lacing should not be crossed on the side running on pulley. (6=widthin inj Cemented Belts. (Formula for canvas and leather.) Gutta-percha, 16 parts* India rubber, 4; pitch, 2; shellac, 1; linseed- oil, 2; melt and thoroughly mix. Leather-Belt Dressing. Use tallow for dry belts, — with the addi- tion of a little resin for wet or dam(3 places. For hard, dry belts apply neats-foot oil and a little resin. Oil drippings destroy the strength of leather. Leather should not be exposed to a temperature much above 110* F. PULLEYS. (Design of.) r = radius of pulley; 6= width of rim = li to liX width of belt; ^» thickness of rim at center, =0.2 to 0.25h: ^i^thicloiess of hub, =0.75hto h; i = length of hub, =6; n = number of arms; A — width of arm at center of hub; Ai = width of arm at rim, =0.8/i; n«=2.54-5r. h=-^ -I- -r-r- -1-0.25 in. Thickness of arms at hub and rim ^g- and -^ respec- 1 tively. (The above for arms of oval cross-section.) Pulleys with more than one set of arms may be considered as separate pulleys combined, with dimensions for each as above, excepting that arm-proportions need be but from 70 to 80% of the values given. Crowning; rise at center of rim = 0.056. Friction Gearing. P = total pressure forcing wheels together at line of contact; F>i = tractive force to overcome friction; /i — coeflScient of friction, =0.15 to 0.20, metal on metal; 0.25 to 0.30, wood on metal; 0.25, leather on iron; 0.2, wood on compressed paper. ROPE TRANSMISSION. 53 Fff/iP; H.P.=FnF-*- 33,000. Transmits power without jar. but is limited to very light loads. ROPE TRANSMISSION. Wire Rope. Used where belting is impracticable, for spans of 70 to 400 feet. Ropes used are 6 strand, 7 to 19 wires per strand. The sheave pulleys have a deep V-groove with a rounded bottom of alternating leather and rubber blocks. The minimum diameters of sheaves for obtaining maximum working tension in rope without overstraining by bending are 150d, 115d, and 90d, for ropes of 7, 12, and 19 wires per strand respec- tively, where rf — diam. of rope in in. Actual H.P. transmitted » 3. Id^, where sheave diams. are ^ above values. Proper deflection in feet» 0.0000695(span in feet) 2. Speeds from 3,000 to 6,000 ft. per min. (i>=ft. per sec.) Manila Rope. Diam. in in., rf= i f * f 1 H H H U 2 21 2i Lbs. per 100 ft. = 9.6 16 20 30 34 42 50 70 112 130 170 192 Ultimate strength in lha. = 9,0O0€P. Safe tension, Tn on driving sidc^ ISOd^Clbs.). Centrifugal force, F= , where w = weight of 1 ft. rope. H.P. transmitted = — ^ysso' * where n»=No. of wraps of rope around pulley. Best economical speed '-=5,000 ft. per min. Add 250 ft. of rope to calculations to provide for tightener. Sheave dimensions: pitch diam. »=40<;{ to 80d; outside diam. »= pitch diam. + 2d + TV in., center to center of grooves = 1.5d; center of groove to edge = d+A in. Cotton Driving Rope transmits about i more power than Manila rope for the same diam. Sides of pulley groove are incUned at 45°; dis- tance from center to center of grooves = 1.5d; width of groove at out- side diam. ■- 1.25d. The bottom of groove is rounded with circle of diam. »• 0.6&2. Sag, B (in inches) is obtained from the following formula: rn=»-g — |-w«, " •= — 5 ^"^Z ^"87"^ ^'' ^^^'^ Z/^length of span in feet. ^ FRICTION. The tractive force necessary to overcome friction between the surfaces of solids depends (1) directly on the pressure between the surfaces in contact; (2) is independent of the area of the surfaces in contact, but increases in proportion to the number of pairs of surfaces ; (3) is independ- ent (at low speeds) of the relative velocity of the surfaces; (4) the trac- tive force depends on the coefficient of friction, /t, for the particular materials employed. Tractive force, Fn^nP. Coeiflcleiits of Friction, /i, for Plane Sliding Surfaces (Morin). (For low speeds and light loads only.) Lubrication. ' Pol- Dry. Water. OUve- j^. Tal- ^ ^ greasy. Wood on wood 0.5 0.68 0.21 0.19 0.36 0.35 Metal on wood 6 .65 .1 .12 .12 1 Hemp on wood 63 .87 Leatner on wood 47 28 Stone on wood 6 Stone on stone 71 Stone on W.I 45 Metal on metal 18 12 .1 .11 15 Leather on iron 54 64 ENERGY AND THE TRANSMISSION OF POWER. Talues of /i for Static Friction (Broomall). Dry. Wet. Dry. Wet. Steel on steel 0.4408 C. I. on C. 1 0.3114 0.3401 Steel on C. 1 23 C. I. on tin 464 Steel on tin 365 C. I. on pine 47 Pine on pine 474 0.635 »» tangent of the angle of friction, i.e., the greatest inclination possible before sliding occurs. If surfaces are thoroughly lubricated the friction is neither solid nor fluid but partakes of the nature of both. Comparison of Solid and Fluid Friction. Solid frictiim varies directly as the pressure and is independent of the area of surface and of velocity (when low). Fluid friction is independent of the pressure, varies directly as the area of wetted surface, directly as t; (at very slow speeds), as v^ (at moderate velocities) and as v^ (at high velocities). For low speeds Morin's table may be used. For flat surfaces, 400 to 1,600 ft. per min., C. I. on C. I., lubricated, u»0.23, at a pressure of 50 lbs. per sq. in. Friction of Journal Bearings (Beauchamp Tower). /i»c>/o-t-p, where t> = Unear velocity in ft. per sec, and p = pressure in lbs. per sq. in. of the projected area of journal. (Projected area = length Xduun.). Values of c vary according to the lubncant employed, \'iz. : Olive-oil, 0.289; lard-oil, 0.281; mineral grease, 0.431; sperm-oil, 0.194- rs^-oil, 0.212; mineral oil, 0.276. These values are for thorough batn lubrica- tion. To avoid seising, p should not exceed 600 lbs. per sq. in. The following results were obtained by Prof. A. L. Williston (E. W. & E., 3-18-06). PL (average). Pressure per Sq. In. Hyatt Roller Bearing. .... .0118 80 to 345 lbs. C. I. Bearing 0608 80 to 250 " Bronae Bearing 112 80 to 146 * ' The bearings were all li in. diam. X4 in., lubricated with moderately heavy machine-oil of good quality. The C. I. and bronse bearings were reamed to size and lapped to insure perfect surface and high polish, fi at starting for the Hyatt bearing was found to be 0.0068. Friction of Collar Bearings. For p»15 to 90 lbs., v«5 to 15 ft., /c= 0.036. Friction Loss in Journals and Collars (A » outside or mean radius for journal and coUar, respectively). Work lost, in ft.-lbs. per min.= FnV''ttPX2nRN, or, expressed in horse-power, H.P . =0.0001904iiPiiV. Work Lost in Pivot Friction -(0.5 to 0.66) (2ffAJNr/iP) m ft.-lbs. LUBRICATION. Spongy metals like C. I., brasses, and white-metal aUosrs, lessen fric- tional resistance to a considerable degree, but the use of imguents is neces- sary for good results. Lubricants are solid, as ra-aphite; semi-solid, as greases; liquid, as oils. The following are the best lubricants for the purposes indicated : Ix>w temperatures: light mineral lubricating oils. Intense pressures: graphite or soapstone. Heavy pressures at slow speeds: graphite, tallow. Heavy pressures at high speeds: sperm, castor, or heavy mineral oils. Light pressures at high speeds: sperm, olive, rape, or refined petroleum oils. Ordinary machinery: lard-oil, tallow-oil, heavy mineral oil. Steam cylinders: heavy mineral oils, lard, tallow. Delicate mechanisms: clarified sperm, porpoise, olive and light mineral lubricating oils. Metal on wood bearings, water. Essential Properties of Good Lubricants. (1) Body or viscosity sufficient to prevent contact of surfaces. (2) Freedom from corrosive acids. (3) As much fluidity as is consistent with body. (4) Low coeffi- cients of friction. (5) High flash and burning points. (6) Freedom from substances likely to cause gumming or oiudation. LUBRICATION. 65 Speelflc Gravities of Lubricants. Petroleum, 0.866; sperm-oil. 0.881; olive- and lard-oils, 0.917; castor-oil, 0.966. Flashing: and Burning Points. Sperm-oil flashes at 400<*F. and bums at 500° F.; lard-oil flashes at 475° F. and bums at 525° F. Tborough lubrication (preferably the oil-bath) is essential in order to obtain the best results, and to prevent seizing. Graphite as a Lubricant. FoUated or thin flake graphite when applied as a lubricant materially reduces friction and prevents seizing and injurious heating of bearings. It may be applied dry to surfaces wliere pressures are light, or mixed with oil or grease (3 to 8% graphite, by weight) for heavy pressures. It may also be used to advantage in the presence of high temperatures, as in steam, gas-engine, and air-com- pressor cylinders, and also in ammonia compressors and pumping-engines. Water of condensation often suffices for a mixing lubricant. Graphite fills up the minute depressions and pores in metal surfaces, brinfi^ng them much nearer to a perfectly smooth condition so that a considerably thinner film of oil (which may have a greater fluidity than usual) will be sufficient. A test of car-axle friction by Prof. Goss (bearing pressure 200 lbs. per sq. in.) gave the following results: Sperm-oil only, 9 drops per min., rise in temp, per hour =26° F.; /£= 0.284 Sperm-oil with 4% of graphite, 12.9 •* " " " " *' *• *' =28° F.; /i= 0.215 (From catalogues of the Jos. Dixon Oucible Co.) Po"wer Measurement. Power is measured by dynamometers, which either absorb or transmit the power undiminished. The Prony Brake is the typical form of absorption dynamometer and consists of a horizontal lever connected to a revolving shaft or pulley in such a manner that the friction between the surfaces in contact tends to rotate the lever-arm in the direction of the shaft rotation. This tendency is resisted by weights on the lever-arm, and the weight that will just prevent rotation is ascer- tained. Let P= weight in lbs. on lever, £ = length of lever in feet from center of shaft to point of application of weight, F = velocity in ft. per min. of point of application of weight if allowed to rotate at the speed of the shaft, iV = r.p.m., and IF™ work of shaft or power absorbed per min. Then, IF-PF-2«Li\rPft.-lb8.,or.H.P.-^^. HEAT AND THE STEAM ENGINE. Heat» according to the dynamical theory, is a mode of motion of the molecules of a substance, its intensity being proportional to the amoimt of motion and its most readily observed effect being that of the expansion of the substance. ' Transfer of Heat. Heat will pass from the warmer of two bodies to the colder until their temperatures become equal, the transfer being effected by radiation, conduction, or convection. Radiation is the transfer of heat from one body to another across an intervening medium whose temperature is not affected by the transfer Dark, rough surfaces are the best radiators and are advantageous in apparatus for heating, while light, polished surfaces are the poorest- Relative Radiating Values. Lampblack, 100; polished metals cast iron, 26; wrought iron, 23: steel, 18; brass, 7: copper, 6; silver. 3 Heat Units Radiated per Hour per Square Foot of Surface (for 1** F. difference in temperature). Pohshed metals: silver, 0.0266; copper. 0.0327; tin, 0.044; zmc and brass, 0.0491; tinned iron, 0.0859; sheet iron. 0.092. Other materials: sheet lead. 0.133; ordinary sheet iron- 0.566; glass, 0.595; cast iron, new, 0.648; do., rusted, 0.687; wrought - iron pipe, 0.64; wood, stone, and brick, 0.736; sawdust. 0.72; water, 1.0853; oil, 1.48. Conduction is the transfer of heat by contact between the molecules of a body or the surfaces of contact of two distinct bodies. Relative Values of Good Conductors. Silver, 100; copper, 73.6; brass, 23.6; tin, 14.5; iron. 11.9; steel, 11.6; lead, 8.5; platinum. 8.4; bismuth, 1.8: water, 0.147. Heat Units Transmitted per sq. ft. per hour, for 1° F. difference in temperature: copper, 643; brass, 557; W. I., 374; C. I., 316 (Isherwood). These values are for bright surfaces up to | in. thick. For surfaces coated with grease or saline deposits (i.e., condensers) Whitham states that these values should be multiplied by 0.323. Relative Values of Poor Conductors as Heat Insulators: Min- eral wool, 100; hair-felt, 85.4; cotton wool. 82; sheep's wool, and in- fusorial earth, 73.5; charcoal, 71.4; sawdust, 61.3; wood and air-space, 35.7. Comparative Radiation from Covered Pipes. Bare pipe, 1.00; covering of magnesia +7% asbestos, 0.308; plaster of Paris 4- 4% asbestos, 0.34. Radiation from Bare W. I. Pipes in B.T.U. per sq. ft. per hour, per degree F. difference of temperature between pipe and surrounding medium (taken at 70° F.): Radiation and Convection 10 50 100 150 200 250 300 Steam-Pipe Coverings. The following figures are for coverings 1 in. thick. (For each iV in. additional thickness (up to 1.5 in.) subtract the percentage given.) Under average conditions (air at about 70°, steam about 66 adiation. Still Air. Moving Air. 0.743 1.247 1.583 0.816 1.55 2.038 0.911 1.773 2.344 1.035 1.983 2.615 1.167 2.18 2.856 1.22 2.4 3.12 1.32 2.6 3.37 MEASUREMENT OF HEAT. 57 100 lbs. pressure) 1 sq. ft. of bare pipe will give off about 3 B.T.U. per hour. B.T.U. radiated per hour per sq. ft. of surface for each deg. F. difference in temperature between steam and outside air (approx.) : Hair-felt, 0.375 (2.6%); Remanit, 0.416 (2%); Manville sectional, best, 6 (1.4%); Magnesia, 0.515 (5.2%); Asbestos sponge, felted, 0.575 (9.2%); Asbestos air-cell, 0.675 (12%); Navy asbestos, 0.7 (8.4%); Asbestos fire, felt, 0.746 (11%). Coverings of 85% magnesia and solid cork coverii^s (1 in. thick) save about 83% of the heat that would be radiated from a bare pipe. Remanit (carbonized silk, wrapped) saves about 87%. Convection is the transfer and diffusion of heat in a fluid effected by the motion of iti^particles. Water in the bottom of a vessel, or air on the floor of a room, being heated, becomes lighter and rises, allowing colder fluid to take its place. Convection currents being thus formed the heat is distributed through the fluid. Expansion results from the apphcation of heat to all bodies. (For coeflicients of linear expansion see foot of page 18.) Water between 32^ and 39.1° F. is an exception to the general law: it contracts as the temperature increases. Cast iron, bismuth, and antimony expand when solidifying, while gold, silver, and copper contract. M easurement of Heat. Temperature is a measure of the intensity of heat and is determined by the employment of a thermometer or a pyrometer. Thermometers. The freezing- and boiling-points of water (under atmospheric pressure) are marked on all thermometers, the space between being graduated as follows: System. Divisions. Freezing-point. Boiling-point. Fahrenheit (F.) 180 32*» 212*» Centigrade (C.) 100 0*» . 100* R6aumur 80 0** 80* whence F' = 1.8C.° + 32 and C.*» = 5(F.«-32). Pyrometers are used to measure very high temperatures, Le Chatelier s being a thenno-electric couple of platinum and platinum-rhodium alloy employed in connection with a galvanometer and caUbrated scale. The high temperatures of furnaces may be approximately ^ ascertained by means of the copper cylinder pyrometer. A small com>er cyhnder of weight w (specific heat =0.0961) is allowed to attain the temperature i° of the furnace and then plunged into a known weight, wi of water whose initial and final temperatures are <*i and T^ respectively. Then, uM(7^-^i°) + 0.0951«;r° ' 0.0951w> Heat Units. The heat motion in a body depends on its mass, heat capacity, and temperature. The British Thermal Unit (B.T.U.) is the amount of heat required to raise the temperature of one pound of water through one desp«e Fahrenheit, the water being near the temperature of its greatest density, 39.1° F. One B.T.U = 778 ft.-lbs. of energy. The Calorie (metric system) is the amount of heat required to raise one kilogram of water one degree Centigrade at or near 4° C. 1 B.T.U — 0.252 Calorie (Cal.). 1 Cal. = 3.968 B.T.U. 1 Cal. - 426.8 kilogram-meters = 3087.1 ft.-lbs. Specific Heat. Bodies, weight for weight, vary in their capacities for absorbing heat. If the heat-absorbing capacity of water is taken as unity, the relative capacity of another substance is called its specific heat and is therefore equal to the amount of heat in B.T.U. required to raise the temperature of one pound of the substance through 1° F. Specific Heats of Various Substances. Water at 39.1° F., 1.00; water at 212° F., 1.0132; ice at 32° F., 0.504; mercury, 0.0333; cast iron, 0.1298; wrought iron, 0.1138; steel. 0.117; copper, 0.0951; coal, 0.24; tin, 0.0562; lead, 0.0314; glass, 0.1976; brass, 0.0939; coal ashes, 0.215. Gases (under constant pressure) carbonic oxide, 0.2479; carbonic acid, 0.217; ammonia, 0.508; air, 0.2375; hydrogen, 3.409. Expansion of Gases. Marriottc*s I^aw. The volume of a given portion of a gas varies inversely as its pressure, if the temperature be con- 68 HEAT AND THE STEAM ENGINE. stant. Koo— ; .. K = -p , aad PV^a. constant. The pressure curve of a gas expanding according to this law is a rectangular hjrperbola and i^ called the isothermal of the gas. Gay-Lussac*s Law. The increase in volume of a given portion of a gas varies directly as the increase in temperature if the pressure be con- stant. Let V, V\, and V2 be respectively the original volume, the increase in volume, and the final volume, and t° the rise in temperature. Then, Fioc^o, and Vi~Vai?, where a— coeflBcient of cubical expansion («coeff. of Unear expansionXS); /. Vi^V+Vi^V+Vat^-VH+a^). « for air = 0.00203611 for each degree F. Absolute Temperature. If a given volume of air at 32° F. be reduced 491.13° in temperature («l-i- 0.00203611), its volume yrill theoretically become zero and its heat-motion may be considered as having ceased. For a perfect gas, absolute sero is 492.66° F. below the melting-point of ice, or, practically, -461° F. (= -273° C), from which point all tempera- tures should be reckoned. In reality, all gases liquefy before reaching absolute aero. Absolute Temperature (t)— 461°+ reading of thermometer in degs. F. Combination of Marrlotte's and Gay-Lussac's Laws. PF«a con- stant, and PVoct; .*. PV = Rt, For 1 lb. of air at 32° F. (12.387 cu. ft.) under atmospheric pressure (14.698 lbs. per'sq. in. » 2,1 16.5 lb«. per sq. ft.), PF = 12.387X2,116.6-26,217.66 ft.-lbs.-Ar, and, as t = 493°. « = 63.354. . . Latent Heat. In changing from solid to liqmd and from liquid to gaseous states, bodies pass through critical points cidled respectively the points of fusion and of evaporation, and at these points heat is absorbed to perform the work of molecular rearrangement. The Latent Heat of a substance is the quantity of heat units absorbed or given out in chang- ing one pound of the substance from one state to another without altering its temperature. Latent Heat of Substances in B. T. U. per Lb. Fusion loe, 142.6 to 144: iron, 41.4 to 59.4; lead, 10.55. Evaporation; Water, 965.7; anmionia, 529; bisulphide of carbon, 162; SO2, 164. Saturation and Boiling Points. Saturation is said to occur when all the latent heat required for steam has been taken up. Boiling occurs when the tension in the water overcomes the surrounding pressure. Dry saturated steam is that which has a specific volume, temperature and pressure corresponding to its complete formation. Wet saturated steam IS that in process of formation and in contact with the water from which it is generated. Superheated steam is that which has its temperature raised above that of the formation point. Specific volume = No. of cu. ft. per lb. Specific density = No. of lbs. per cu. ft. Moisture in Steam is measured by a calorimeter, and the percentage Tf TT Jr( T^ f^'\ ~ of moisture, u»=100X ^—7 » where fl^= total heat, L« latent heat per lb. of steam at the pressure of the supply-pipe, .£fi"» total heat Eer lb. at the pressure of the discharge side of calorimeter. A; = specific eat of superheated steam, 2"° = temperature of the throttled superheated steam in the calorimeter, and <° — temperature due to the pressure (m the discharge side «°»212°F. at atmos. pressure and A; =0.48). All but ^ to 1% of the moisture in steam may be removed by the use of a separator, in which apparatus the direction of steam flow meets with abrupt changes and the water particles by reason of their momentiun are thrown out of the path of flow. The Quality of Superheated Steam (or the percentage of heat in excess of that due to the pressure), Q=«[L+0.48(5r°-<°)]-5-L, where I/ = latent heat of 1 lb. of steam at the observed pressure, r° = observed temperature, and <° = temperature due to pressure. Pressure and Temperature Relations of Saturated Vapor. Log p-a + ba^-f ciJ" (Regnault). 32° to 212° F. 212° to 428° 32° to 212° 212<» to 428° a = 3. 025908 3.743976 I log a = 9. 998181-10 9.9985618-10 log 6 = 0.61174 0.412002 log /9 = 0.0038134 0.0042454 log c= 8. 13204-10 7.74168-10 J n=<°-32 <°-212 SENSIBLE HEAT. 59 Rankiiie gives as a dose approxiinatioii, log p^A ,, where il -6.1007, iosB-3.43642, losC»5.59873. and p»lb8. per sq. in. (in both fonnulas). Sensible Heat, — Heat of the Liquid (h). The number of B.T.U. required to raiae 1 ib. of water from the freesing-point to 1° Centigrade »■ (* + 0.00002<»^+0.0000003e) X 1.8. The Total Heat of Eyaporatlon is the quantity of heat necessary to raise one pound of water from 32*^ F. to a mven temperature and then evaporate it. Total heat (in B.T.U.) =l,09r7+0.305««-32)- 1,081.94 +0.3(>5f'. Latent heat = total heat ~ sensible heat « (approximately) 1,001.7— 0.605(1°— 32). (For greater accuracy subtract the sensible heat as obtained from formula above from the total heat.) Density (i>), Tolume (V), and Relative Volume (Vr) of Satu« rated Steanu The density or wei^t in lbs. of 1 cu. ft. of saturated steam may be obtained from log x>» 0.941 log p — 2.510. The volume <A 1 lb. of steam in cu. ft. may be obtained from log F=" 2.519 —0.941 log p. The relative volume or number of cubic feet of steam from 1 ou. ft. of water may be derived from log Vr- 4.31388 -0.941 log p. The External Work of 1 lb. of Steam, TF, (in B.T.U.) - 144p^cu.ft.inl lb.rteamatp.-0.016) ^^^ o.016=cu. ft. in 1 lb. of Evaporation from and at 212°. In compaiing the evaporative performances of boilers working under various pressures and tempera- tures, it is customary to reduce them to a normal standard efficiency expressed by the equivalent weight of water which would be converted into steam if it were supphed to the boiler at a feed temperature of 212^ and evaporated at the same temperature and at atmospheric pressure. The equivalent weight of water evaporated "from and at" 212^, TT— Tjggy. where If —total heat of the steam generated at the given abso- lute pressure (gauge pressure + 14.7 lbs.) and A«the heat of feed- water. Properties of Saturated Steam. The following table is abstracted from the complete tables of Prof. C. H. Peabody. whose results are probably in more general use among engineers than any others. ^-* total heat of the steam- 1,091.7 4-0.305(^-32); A -heat of the liquid; L- latent heat of vaporisation, -»£r— A. Internal work, TTi— 1»— r-r, where u — 1>— 778 .016— increase of volume of water and steam during evaporation (1 lb. water— .016 ou. ft.). Entropy of liquid ^io— specific heatXlog^-^; L ^ entropy of vapor, ^« — +^tt,; t-<**-1-460.7. p (absolute) -pressure above vacuum in lbs. per sq. in.; v — vol. of 1 Ib. of steam in cu. ft.; IT — weight of 1 cu. ft. of steam in lbs. The values above 325 lbs. pres- sure are from Buel's tables. Coollns Water Required by Condensers. Heat lost by steam-heat gained by the water; or, lbs. steam X (sensible heat -I- latent heat — temp, of hot well) = lbs. water X (final temp, of water— initial temp, do.), which may be redused to. lbs. water per lb. of steam, w =(1 113.94 -I- .3055r« ^Th)-*-(Tw-'tw), where r«-temp. of steam at release, Th = temp.o{ hot-well (usually from 110 to 120° F.), Tw and ^u;— final and initial temps, of the cooling water. This formula has been criticised by E. R. Briggs (Am. Mach., 5-18-05) because it assumes that the whole weight of entering steam must give up its heat of vaporization at the release temperature, when, as a matter of fact, some 20 to 30% of the steam is in the form of water at this point. He suggests the following formula which gives much smaller results. u»— (H—-'^ -)-!-( ru) — M, where fl^- total heat per lb. of steam sup- {)lied to engine (reckoned above Th), a; — steam consumption of engine in bs. per I.H.P. hour, and 2,545 -B.T.U. in one H.P. per hour. Specific Heats of a Gas. The specific heat (kp) at constant pressure of any normally permanent gas such as air is 0.2375 B.T.U. 60 HEAT AND THE STEAM ENGINE. Properties of Saturated Steam. p (abs.). 1^¥. V. w. H. h. L. 0.5 80 640.8 .00158 1106.3 48.04 1058.3 1 101.99 334.6 .00299 1113.1 70 1043.1 3 141.62 118.4 .00844 1125.1 109.8 1015.3 5 162.34 73.22 .01336 1131.5 130.7 1000.8 10 193.25 38.16 .02621 1140.9 161.9 979 14.7 212 26.42 .03794 1146.6 180.9 965.7 15 213.03 26.15 .03826 1146.9 181.8 965.1 20 227.95 19.91 .05023 1151.5 196.9 954.6 26 240.04 16.13 .06199 1155.1 209.1 946 30 250.27 13.59 .0736 1158.3 219.4 938.9 35 , 260.85 11.45 .08736 1161 228.4 932.6 40 267.13 10.37 .09644 1163.4 236.4 927 45 274.29 9.287 .1077 1165.6 243.6 922 50 280.85 8.414 .1188 1167.6 250.2 917.4 55 286.89 7.696 .1299 1169.4 256.3 913.1 60 292.51 7.096 .1409 1171.2 261.9 909.3 65 297.77 6.583 .1519 1172.7 267.2 905.5 70 302.71 6.144 .1628 1174.3 272.2 902.1 75 307.28 5.762 .1736 1175.7 276.9 898.8 80 311.8 5.425 .1843 1177 281.4 895.6 82 313.51 5.301 .1886 1177.6 283.2 894.4 84 315.19 5.182 .193 1178.1 285 893.1 86 316.84 5.069 .1973 1178.6 286.7 891.9 88 318.45 4.961 .2016 1179.1 288.4 890.7 90 320.04 4.858 .2058 1179.6 290 889.6 92 321.06 4.76 .2101 1180 291.6 888.4 94 323.14 4.665 .2144 1180.5 293.2 887.3 96 324.64 4.574 .2186 1181 294.8 886.2 98 326.12 4.486 .2229 1181.4 296.4 885 100 327.58 4.403 .2271 1181.9 297.9 884 102 329.02 4.322 .2314 1182.3 299.4 882.9 104 330.43 4.244 .2356 1182.7 300.9 881.8 106 331.83 4.169 .2399 1183.1 302.3 880.8 108 333.2 4.096 .2441 1183.6 303.8 879.8 110 334.56 4.026 .2484 1184 305.2 878.8 112 335.89 3.959 .2526 1184.4 306.6- 877.8 114 337.2 3.894 .2568 1184.8 308 876.8 116 338.5 3.831 .261 1185.2 309.4 875.8 118 339.78 3.77 .2653 1185.6 310.7 874.9 120 341.05 3.711 .2695 1186 312 874 125 344.13 3.572 .28 1186.9 315 871.9 130 347.12 3.444 .2904 1187.8 318.4 869.4 135 350.03 3.323 .3009 1188.7 321.4 867.3 140 352.85 3.212 .3113 1189.5 324.4 865.1 145 355.59 3.107 .3218 1190.4 327.2 863.2 150 358.26 3.011 .3321 1191.2 330 861.2 155 360.86 2.919 .3426 1192 332.7 859.3 160 363.4 2.833 .3530 1192.8 335.4 857.4 165 365.88 2.751 .3635 1193.6 338 855.6 170 368.29 2.676 .3737 1194.3 340.5 853.8 175 370.65 2.603 .3841 1195 343 852 180 372.97 2.535 .3945 1195.7 345.4 850.3 190 377.44 2.408 .4153 1197.1 350.1 847 200 381.73 2.294 .4359 1198.4 354.6 843.8 210 385.87 2.19 .4565 1199.6 358.9 840.7 220 389.84 2.096 .4772 . 1200.8 363 837.8 230 393.69 2.009 .4979 1202 367.1 834.9 240 397.41 1.928 .5186 1203.2 371 832.2 250 400.99 1.854 .5393 1204.2 374.7 829.5 260 404.47 1.785 .5601 1205.3 378.7 826.6 275 409.5 1.691 .5913 1206.8 383.6 823.2 300 417.42 1.554 .644 1209.3 391.9 817.4 325 424.82 1.437 .696 1211.5 399.6 811.9 500 467.4 0.942 1.062 1224.5 443.5 781 1000 546.8 0.48 2.082 1248.7 528.3 720.4 SPECIFIC HEAT AT CONSTANT VOLUME. 61 The specific heat at constant volume (kv) is less, no external work being performed, and is equal to 0.1689 B.T.U. Expressed in foot-pounds, and using capitals for symbols, Xp = 184.77 ft.-lbs., and iiCr- 131.42 ft.-lbs. The specific heat of a gas at constant pressure is the same at all tem- peratures. External work =» P( V, — V ) = it (ti — r) . Total heat=iiCp(Ti-T); .*. Internal work-^iKp-RXn-x). When a gas is heated at constant volume only internal work is done consequently iJCp—iCv^ 12 = 53.354 ft.>lbs. The Specific Heat of Superheated Steam at constant pressure is usually taken as 0.4805. Gnndley states that it averages from 0.4317 (between 230° and 246° F.) to 0.6482 (between 295° and 311° F.). Assum- ing a straight-line equation between these values, Specific Heat of super- heated steam, kpi&t ^) =0.3461 -l-0.00333(<°- 212). Griessman (Z.V.D.I., 12-26-03) gives A;p = 0.375 + 0.002083(<°- 212). Prof. C. R. Jones (E. R., 7-16-04) gives Ai,=0.462-l-0.001525p, where p = absolute pressure in lbs. per sq. in. H. Lorenz (Z. V.D.I. , No. 32-04) employs the following formula, where A^ varies as the pressure and inversely as the cube of the absolute temperature: A^ =0.43 + 1,476,000-^ (p in lbs. per sq. in.; r =461° +<° Fahrenheit). By making fair suppositions as to the temperatures involved in Jones' experiments, his results agree fairly well with those of Lorenz. For low pressures the value of Regnault (0.4805) seems corroborated by these investigators, while for pressures around 120 lbs. a value of 0.6 may be taken. Kp for superheated steam (when Ajp =0.4805) = 373.83 ft.-lbs., and Xt,^ 288.05 ft.-lbs. ii:p-Xt; = 85.78 ft.-lbs. and Xp-i-ii:t;= 1.3. The total heat of superheated steam, Hi='H-hkp(ta—t), where H is the heat at tem- perature^ of the steam at saturation and ts is the temperature attained in superheating. Expansion Curves. Adlabatlcs and Isothermals. The area A included by the ordinatea P and Pi, the axis of abscissas and the curve of formula PF=PiFi = C is: A=Py loge (Fi + y) = /eT loge (Fi^y) = Rrloger, where r= ratio of expansion. When the curve is of the form PFn-PiFi-^C. A-(PF-PlFl)-^(n-l). n = r-(Kp+Kv) of the sub- stance employed in the expansion. When a ^as expands against a resistance it performs work which requires an expenditure of heat. If the gas itself yields this supply of heat its temperature is lowered and the expansion is called adiabatic and repre- sented by PV** = C. If the heat required during the expansion be sup- plied from an external source the temperature of the expanding gas remains constant and the expansion is termed isothermal (PV^C). Various Expansion Curves. Isothermal of a perfect gas: PV'^C. Adiabatic of a perfect gas: PV^^'C. (r = 1.3 for superheated steam and 1.408 for air — usually taken as 1.41). Expansion of dry, satiu'ated steam without becoming either wet or superheated: pF^' = 475 (Rankine), or (p-f-0.35)(F- 0.41) = 389 (Fairbaim). Adiabatic of saturated steam: &F" = C where n= 1. 035 -H 0. 1 X dryness fraction, the dryness fraction sing the weight of the sf-eam after the water particles are subtracted, divided by the weight of both steam and water particles. n = 1.135 for initially diy steam (Zeuner) and n = 1.111 for steam containing 25% of moisture (Rankine). (For additional relations between p, v, and t see Compressed Air.) Specific Volume of Dry Saturated Steam. F= — -\-v. Take rp f° at 1°, find the increase of pressure p from tables for 1°. v = vol. of 1 lb. of water, in cu. ft. L = latent heat at t° F. (absolute), in ft.-lbs. Volume of Superheated Steam. If greater than that of saturated steam, PF„p. = 93.5T,„p.-971P«-25 (Peabody). Thermal Efficiency of Heat Engines. Efficiency =^^^^, where t is the absolute temperature at which the heat is received (which should be as near to that of the furnace or gas explosion as possible), and ti the 62 HEAT AND THE STEAM ENGINE. absolute temperature of rejection of the heat, i.e., that of the condenser or the atmosphere. If ti were absolute sero, the efficiency would be the maximum attainable. Tue difference, therefore, (t— ti), should be the greatest possible with available temperatures. Causes of Energy Loss in Steam Engines. Steam is not supplied at the furnace temperature (the greatest cause of loss), and the tempera- ture of rejection is higher than that of the cooling water in the condenser. Steam is not compressed from the condenser temperature to that of the furnace, only a small part being compressed to the temperature correspond- ing to boiler pressure. If the condensed steam is not returned to the boiler a corresponding weight of feed-water must be heated to boiler tem- perature. Initial condensation in the cylinder causes waste, only a por- tion of the steam so condensed being re-evaporated during the stroke, and the expansion is not adiabatic. Clearance in the cylinder requires an additional amount of steam for each stroke which performs no work dur- ing the full pressure period of the- stroke. Water particles in the steam, (due to boiler priming) pass into the condenser without performing work and also abstract heat from the cylinder in their attempt to vaporixe. T must not be high enough to bum the cylinder lubricant or the packing and Ti is limited by the temperature of available condensing water. Radiation, leakage of steam, receiver drop in compoimd engines, wire- drawing, and friction losses (both of steam now and of the moving parts of the engine) are additional causes of loss. Initial Condensation. When saturated steam is admitted to a cylinder which has been cooled to exhaust temperature, part of it con- denses. After cut-off the condensation continues, but, as the cylinder and steam temperatures become more nearly equalized, the latent heat liberated during liquefaction causes a partial re-evaporation. The initial loss is considerable, and, being but partially recovered through the re- evaporation, a quantity of water is rejected at release, part of which evaporates during the exhaust and causes back -pressure. Methods of Beducing Cylinder Condensation. If the engine has a high rotating speed the time of each stroke is too short to allow the temperature changes which cause condensation to take place. Clothing the cylinder with non-conducting materials is a partial means of preven- tion. The supply of heat from live steam to tne walls of the cylinder by means of a surrounding jacket assists re-evaporation providing that the piston speed is low enough to permit the absorption of the heat. By compounding, the work is divided among 2 to 4 cylinders and the range of temperature in a single cylinder is comparatively small. The saving due to compounding results from the re-evaporation taking place earlier in the total expansion. The use of superheated steam is the most effective preventive of con- densation. Saturated steam is allowed to flow through a coil or other form of superheater, its temperature being there sufficiently raised by the heat of the furnace gases to keep it dry, or nearly so, during the stroke. Superheat cannot exceed 750° F., cylinder lubrication being impossible at higher temperatures ; the best results, however, are obtained between 650° and 700°. With superheat the pressures do not need to be so high, 160 lbs. being ample excepting in the largest engines. A moderate super- heat of 100° to 150° above boiler temperature aids, especially in long pipe transmissions, and effects a saving of 10 to 12%. At 120 lbs. pressure, with 170° superheat, 18% of the steam-consumption has been saved in a triole-expansion engine. A saving of 50% has Deen recorded, but 15 to 25% more nearly represents average practice. The following formulas approximately express the results of a large number of tests (»S=»saving{ m per cent): 5=5.17 + 0.083 Xdegs. F. of superheat (for turbines); 5=4 + 0.12 Xdegs^ F. of superheat (for reciprocating engines). Heating Surface of Superheaters. A (in sq. ft.)= ' Qf^ L^ \ * where 0.48 = sp. heat of superheated steam, TF = lbs. of steam to be suiter- heated per hour (boiler temp., ^2)1 <i=temp. after superheating, tg^^temp. of furnace gases (1,000° to 1,200° F.), 6 = B.T.U. transmitted per sq. ft. of heating surface per hour, where ih-tO —400° to 500° F, INDICATOR DIAGRAMS. 63 Leakage is nearly independ^it of speed of sliding surfaces, is propor- tional to difference of pressure between the two sides of valve, and is inversely as the overlap of valve. With weU-fitting valves it may amount to over 20% of the entering steam, and rarely falls below 4%. For an un jacketed cylinder with a given ratio of expansion, initial con- densation (expressed as a percentage ofthe steam in the cylinder) diminishes with increase of initial temperatiue, while the total condensation per stroke increases with such temperature increase. Re-evaporation for a given ratio of expansion is as great, and sometimes fi;reater, without jackets as with them, showing clearly that the regenera- tive action of the cjrlinder walls with a given ratio of expansion is largely independent of their mean temperature. (Prof. Capper, in Report of Steam-Engine Research Com. of I.M.E., 1905.) Calculation of Initial Condensation and Leakage* Steam not accounted for by indicator c log< r Indicated steam ' ^fy^ * where r— ratio of expansion, c— 6 to 8 for simple unjacketed engines, 4 for jacketed slide-valve engines, 2 to 4 for Cx>rliss engines (jacketed and imjacketed, respectively), and 12 for very poor engines. Indicator Diagrams. (Fig. 11.) The fi^pue shows the indicator dia- gram of a simple condensing engine, ON bemg the vacuum line or line FSg.ll. of aero pressure, 08 the line of sero volume, and JD the atmospheric line of 14.7 lbs. absolute pressure (0 lbs. gauge). AR is the length of stroke and 8 A the clearance, which is the volume of the valve passages plus the volume between the piston at the end of stroke and the cylinder head reduced to a percentage of the stroke. (Clearance ranges from 2 to 7% of the total volume; when unknown it may be assumed as being 3% for well designed engines.) The clearance space first fills, pressure rising immediately to A^ and the piston moves to jB. where the steam is cut off, and expansion tiJces place between B and C. If the cut-off is gradual (due to slow closing ol the steam port), the steam will be "wire-drawn," and the pressure before cut-off will fall along the line AB'. The exhaust port opens at C and the pressure drops to D and on the return stroke through D to B, where the port is fully open, and remains so until F is reached. The exhaust port closing at F, the remaining steam is compressed to O (cushioning the stroke), where incoming fresh steam, (due to the opening of steam-valve slightly before the commencement of the next stroke), rapidly raises the pressure to the starting-point A. The space V between the lines FE and ON represents the back-pressure 64 HEAT AND THE STEAM ENGINE.^ - . i due to vapor pressure in the condenser, it being impossible to obtain a peiiTect vacuum. Back -pressure varies from 2 to 3 lbs. under fair condi- tions. The theoretical expansion curve BMT is an equilateral hyperbola (assuming the expansion to be isothermal) and should be drawn on the diagram or card for comparison. Taking any point M on the actual expansion curve B'MC, draw KM perpendicular to SR and intersecting it at K. Draw OK, and also AfL parallel to SR and intersecting OK at L. Draw LB perpendicular to SR. B will be the theoretical point of cut-ofif. Any other point (M') may be determined by drawing OK'; then a perpendicular let fall from K' will intersect UM' (drawn parallel to SR from intersection of OK' and BL') at M', the desired point. Where the clearance is unknown it may be approximately fixed by selecting two points on the expansion line (B, M'), drawing the rectangle BK'M'U and producing the diagonal K'U to its interisection with ON at O. Faults shown by Indicator Cards. (Fig. 12.) A, — too early admis- sion; S, — too early release; C, — too early compression; Z), — ^too late release; E, — too late admission; F, — too little compression; G, — too early cut-off; H, — choked admission; J, — choked exhaust; K, — ^lesJcy cut-ofiP; Z/.^too much back-pressure; Af,— double admission; N, — eccen- tric slipped backward; O, — eccentric too far ahead; P, — indicator inertia; Q, — sticking indicator piston; JB, — ^initial condensation; *S, — re-evapora- tion. T shows the form of card obtained from gas-engines, the heavy line being the theoretical card. The explosive charge is drawn in along the atmospheric hne, compressed along the lower curve, and ignited at the end of compression, when the pressure rises instantly. Expansion takes place along the upper curve to point of release, where the exhaust is then represented by the atmospheric line to the point of beginning of the cycle. In actual cards the ignition is not instantaneous but takes place along the dotted curves, the lower one indicating too late ignition and consequent loss of power. Release takes place before the end of the stroke, the pressure falhng as shown by dotted Une. Calculation of Indicated Horse-Power. I.H.P.=^^^^^\ where Vm is the mean effective pressure throughout the stroke, in lbs. per sq. in., Z/ = stroke, in feet, o = area of piston, in sq. in., and 2iV' = No. of strokes per minute. To obtain Vm (also abbreviated to m.e.'p,), find the area of the card or diagram by means of a planimeter and divide same by its length, thus obtain- ing the mean (or average) height, and- express this height in lbs. of pres- sure by comparison with the scale of the spring used in the indicator. Or, divide ARNQ (Fig. 11) into 10 equal parts by vertical lines, measure the middle ordinate of each on the diagram, add same and divide by 10, thus obtaining the average height. Or, trace the card on section-ruled paper, ascertain the number of squares included by the boundary-line of the diagram and divide this number by the number of squares in one horizontal row between the extreme end ordinates of the diagram, thus obtaining the mean height. Should there be a loop in the diagram (as in Fig. 12 for too early cut-off) its area should be subtracted from the re- mainder of the diagram as the pressure indicated by the loop is negative. Vacuum. — The best vacuum for a reciprocating engine is from 24 to 26 in. when the barometer is at_30 in. ; _ with a better vacuum the additional gains are offset by the losses in obtaining same. A turbine should have the best obtainable vacuum, each additional inch above 24 in. reducing the steam consumption some 4 to 6%. Indicated Water Consumption. — Lbs. water per hour per I.H.P. = 137.5[(fe + c)ty~cti;]]-J-p^, where 6 = percentage of stroke -completed at point where the calculation is made (which may be at any point between cut-ofif and release); c = percentage of clearance to the stroke; «? = weight in lbs. of 1 cu. ft. of steam^ at the pressure of the point where the cal- culation is made; rf;i = lbs. in 1 cu. it. of steam at the final compression pressure. Diagram Factor. In a theoretical diagram with admission at boiler pressure (p) up to the point of cut-ofT, expansion along a hyperbolic curve, release at the end of stroke, exhaust at back-pressure (Pb), and no compression, Pni = — (H-log« r^ — pb, where r= ratio of expansion*- number DIAGRAM FACTOR. 66 of volumes the original volume has expanded to, p and Ph beins absolute pressures. The actual Pm of an engine may be foimd by multiplying the right- hand member of the above equation by c, the diagram factor. Fig. 12 Values of c : 0.78 for simple, unjacketed, slide-valve engines. Com- poimd engines, — 0.6 to 0.8 for high-speed, unjacketed; 0.7 to 0.85 for 66 HEAT AND THE STEAM ENGINE. low-speed, un jacketed; slow-speed, jacketed, 0.85 to 0.9. Corliss, jacketed. 0.8 to 0.9. Triple-expansion, — high-speed, unjacketed, 0.7 ; marine engines, 0.6 to 0.66. Hyperbolic Logarithms. No. Log. No. Log. No. Log. No. Log. 1 5.25 1.6582 9.5 2.2513 25 3.2189 1.25 .2231 5.5 1.7047 9.75 2.2773 26 3.2581 1.5 .4055 5.75 1.7492 10 2.3026 27 3.2958 1.75 .5596 6 1.7918 11 2.3979 28 3.3322 2 .6931 6.25 1.8326 12 2.4849 29 3.3673 2.25 .8109 6.5 1.8718 13 2.5649 30 3.4012 2.5 .9163 6.75 1.9095 14 2.6391 31 3.434 2.75 1.0116 7 1.9459 15 2.7081 32 3.4657 3 1.0986 7.25 1.9810 16 2.7726 33 3.4965 3.25 1.1787 7.5 2.0149 17 2.8332 34 3.6263 3.5 1.2528 7.75 2.0477 18 2.8904 35 3.5553 3.75 1.3218 8 2.0794 19 2.9444 36 3.5835 4 1.3863 8.25 2.1102 20 2.9957 37 3.6109 4.25 1.4469 8.5 2.1401 21 3.0445 38 3.6376 4.5 1.5041 8.75 2.1691 22 3.0911 39 3.6636 4.75 1.5581 9 2.1972 23 3.1355 40 3.6889 5 1.6094 9.25 2.2246 24 3.1781 Diameter of Cylinder for any given I.H,P. d = 144.9 Vl.H.P.-!-PmLiV. Cylinder Batios for Multip le Expansion E ngines. — For com- pound engines (2 cyls.), ratio — VNo. of expansions = 2.8 to 3.6. For triple expansion engines: Gauge Pre«.u«. High^ ^ter^ ^^^Low^ 130 lbs 1 2.25 5 140 " 1 2.4 5.85 150 " 1 2.55 6.9 160 •• 1 2.7 7.26 For quadruple expansion engines: Gauge Pre»u«,. Hi^^,f- ^^^: ^g-" Low. 160 lbs 1 2 4 8 180 " 1 2.1 4.2 9 200 *• 1 2.15 4.6 10 220 •• 1 2.2 4.8 11 The most economical point of cut-off in a simple, non-condensing engine lies between i and ^ of the stroke. The Best Batio of Expansion. The best number of expansions (N) in a simple condensing engine is iV=-T^(log« — H — ), where x and n are absolute temperatures, V and Vi are vols, in cu. ft. of 1 lb. of steam, L and Z/i are latent heats. V, r, and L for the beginning and Fi, ti, and Li for the end of the expansion (Willans). Combination of Multiple Expansion Diagrams. In order to com- pare the expansion with any desired theoretical curve, the several dia- grams of the multiple expansion cylinders must be plotted on the same horizontal scale of volumes, clearances being added to the volumes proper. Any reference curve R may then be drawn. (Fig. 13). STEAM CONSUMPTION OF ENGINElJ. 67 Steam Consumption of Engines. Boiler Pres- Lbs. Steam Type. I.H.P. sure. Lbs. per I.H.P. per Sq. In. per Hour. Nan-Oondensinff : Common Slide-valve 25 to 100 80 33 to 40 Single-valve Automatic, high speed 60 "160 80 32 " 40 Double-valve Automatic, hich speed 60 "160 80 30 " 85 Field, with superheat 136 113 (18.6) Corliss. Automatic 100 to 200 75 to 90 22 to 27 (17.5) Compound " .high speed.. 100 *' 250 110 " 120 25 " 27 Condensing: Coriiss. Simple 200 and up 80 18 to 20 Compound Automatic. « high speed 200 to 500 110 to 120 17 " 19 Compound Schmidt (superheat) 75 180 (10.17) Corliss 400 and up 110 to 135 13 to 17 Leavitt 640 135 (12.16) Bollinckx 300 90 (12.19) Triple Expansion, Marine and Pumping 300 to 1,000 160 to 180 11 .2 to 15 Triple Expansion, Sulaer 615 140 (11. 85) .AUis 575 120 (11.68) Quadruple Expansion 180 to 200 10 to 12 Rice & Sargent Ooss-compound. . . 420 143 . 4 (9 . 56) (Vacuum, 26.8 in., superheated to 443'* F., Cyls., 16.07 in. and 28.03 in. (r =3.04)) (at throttle) Lbs. per E.H.P. Hour. Westinghouse - Parsons Turbine, (Vacuum, 28 in., superheat, lOO'' F., 3,500 r.p.m..fuirioad).. 553 150 13.55 Same (superheat, 140**^, 1,500 r.p.m.) 2,030 160 12.66 Same (saturated steam, 1,500 r.p.m.) 2,030 150 14.7 (A gain of 14% by superheating. Consumption at naif load is 9% greater.) The values in parentheses are some of the most economical results ever obtained. These figures may be expected from first-class designs: non- condensing, 25 lbs.; condensing- simple, 18 lbs.; compound, 16 lbs.; triple expansion, 13.5 lbs. The following are some recent economical results with saturated steam: Westinghouse-Parsons Steam Turbine (Dean & Main test). 600 H.P., saturated steam at 150 lbs., 28 in. vacuiun: 125% load, 13.62 lbs. steam: 100% load 13.911bs.; 75% load, 14.48 lbs. ; 41% load, 16.05 lbs.; average. 85% load, 14.51 lbs. steam per H.P. 850 H.P Rice & Sargent compound Corliss en^ne, 120 r.p.m.* cylinder ratio, 1:4; clearances 4% and 7%; live-steam jackets on cyl. head, live steam in reheater. For 600 H.P. load (150 lbs., 28.6 in. vacuum, 33 expan- sions) Prof. Jacobus' test showed a steam consumption of 12.1 lb. per H.P. hour. The cyl. condensation loss was 22% and the jacket con- sumption 10.7% of the total steam used. 250 H.P. Van den Kerchove compound engine, with poppet valves; 126 r.p.m., cylinder ratio, 1, 2.97: clearances 4%, jackets all over cylinder, no reneater. For 117 H.P. load Prof. SchrOter's test showed a steam consumption of 11.98 lbs. per H.P. hour (150 lbs. pressure, 27.6 vacuum, 32 expansions). The cyl. condensation was 23.5% and the jacket consumption 14% of the total steam. The most economical encine reported is a Cole, Marchent & Morley vertical cross-compound, with un jacketed cylinders and having a receiving reheater between. Nominal H.P. « 500; cylinders, 21 and 36 in., stroke. HEAT AND THE STEAM ENGINE. 36 in. Boiler pressure, ( = 378° superheat). R.p.m. = 100.7; I.fl.P. = 145.5. Vacuum' 26.5 in. Steam per I.H.P. per hour = 8.585 lbs., and at 481 I.H.P., 9.098 lbs. The engine is supplied with drop piston valves, and ha^ run successfully for 114.5 lbs. gauge, temperature of steam, 726** F. R.p.m. = 100.7; I.H,P.= " Fig. 13. over a year, no trouble being experienced with the high temperatures employed. (The Engineer, London, June 2, 1905.) Governors. Simple Fly-ball or Watt Governor. Let A — vertical distance from the point of support of the radius or pendulum arms to the plane in which the centers of gravity of the balls or weights revolve at any particular speed. Then, h~ — ^7^— inches, and N= — —. Greater sensitiveness may be obtained by using the Porter type of governor, which has an axial weight wi in addition to the fly-ball weights (each">tt;) of a , , ^, . , /iy + iyi\ 35,200 . simple governor In this case h — I ^ ) — rj^~ m. \ w / jN* Valves. Zeuner's Diaeram. When the crank is on the dead-center the normal slide-valve A should be at half -stroke, 90° in advance of the crank and on the point of admit- ting steam. If the valve has steam lap B added to it, the advance would necessarily be 90° + steam lap. To assist the steam under compres- sion in cushioning the stroke, steam is admitted slightly before the end of stroke and at the dead-center the valve is then open by an amount called the lead, which must be added to the advance (90° + steam lap), to locate the position of the eccentric. Steam and exhaust laps {B and C) form an additional width to the valve-face and are for the purpose of effect- ?ng an early cut-off of steam or exhaust flow. (Fig. 14.) W//J///////, Fig 14. ZEUNEBS VALVE DIAGRAM. 69 The iMstion of a slide-valve is best shown by means of Zeuner's diagram (Fig. 15). On the diameter AF( = 2Xeccentric throw) draw the circle ABFH. In the small diagram (I.) draw the steam- valve circle OF and also the exhaust- valve circle OA. With O as a center draw an arc with radius OAf( = steam-lap) and also an arc with radius 0/2(= exhaust-lap) If the crank is on the dead-center A^ the eccentric will be at B, or 90°+^ in advance. The intercepts or shaded part MF made by the radius OB f^Mjf 1 Fif.|& on the steam- valve circle will show the amounts of port openhig for the corresponding positions of OB, or the eccentric. The diagram may be used to better advantage by turning the valve- circles hack 90** + 9, as in the main figure. Steam is admitted before the end of the previous stroke, the crank position being shown by OK which passes through the point N. The angle AOK is tne angle of lead. At OA the crank is on a dead-center, at OB the steam-port is fully open and at OD steam is cut off by the closing of the port. From D to J^ the steam expands in the cylinder. At E the exhaust-port opens, reaching full opening at O and closing at J , the steam remaining in cylinder being com- pressed to K, where fresh steam is admitted for the next stroke. OM is the steam-lap, OB the exhaust -lap, and LM is the linear lead due to the angular lead AOK. WY \9 the width of the steam-port and the exhaust has full opening from OF to OT. (O is center of circle ABF.) 70 HEAT AND THE STEAM ENGINE. By increasiiig the steam-Isp, admission takes place later in the stroke and ceases earlier; expansion occurs earlier and ceases later; exhaust and compressicm are unchanged. By increasing the exhaust-lap admission is unchanged, expansion begins 98 usual but continues longer, exhaust occurs later and ceases earlier, and compression begins earlier and ceases later. By increasing the travel of the valve, admission begins earlier and ceases later, expansion occurs later and ceases earlier, exhaust begins and ceases later, and compression begins later and ends earlier. By increasing the angular advance, admission, expansion, etc., all begin earlier but their respective periods are unaltered. Talve Proportions* Ports should be dimensioned so as to allow a velocity of about 6,()00 ft. per min. for live steam, and about 5,000 ft. per min. for eidiaust. For a velocity of 6,000 ft. per min., Port area - (diam. of cyU^Xpiston speed Le„,th of port should be as ne« diam. of cyl. as possible, and width » area + length. Width of exhaust port ■= ^^n^ + width of steam-port — width of bridge between ports + ex- haust lap. For Corliss cylindrical semi-rotary valves; diam. of admission- valve <» 3.2 X width of steam-port ; diam. of exhaust-valve = 2.25 X width of exhaust- f>ort. Length *= diam. of cyl. Widths to be obtained from area formula or slide-v^ves. Piston Speeds in Feet per Minute. Locomotives, 1,000 to 1,200; marine engines, 700; horisontal engines, 400 to 600; pumping-engines, 130. Cyl. area + port area ■= 6,000 -s- piston speed in ft. per min. Flow of 'Steam. Lbs. per min. «0.85ap when dischargine into the atmosphere. When flowing from one press ure to a nother which is d lbs. less and p—d>.68p, lbs, per min. = 1.9oA;'^(p— d)d. A; =0.93 for a short nozzie and 0.63 for an orifice in a thin plate (p=« absolute pressure). Also, velocity in ft. per sec. =-3.5953>/^ when A = height in feet of a column of steam of the given absolute initial pressure and of uniform density, whose weight is equal to the pressure on th e uni t of base. Flow of Steam In Pipes. t>=50y -y-, where L and D are the length and diameter of the pipe in feet and H is the height in feet of a columv of steam at entrance pressure which would produce a pressure equal t4 the difference between the press ures at the ends of the pipe. Q, in cu. ft. per min.=4.7233T -y—-, where rf—diam. of pipe in inches Wt in lbs. flowing per i][iin.=87i/ -^ — o^r where w— lbs. per cu. fi y L(i+M) of steam at initial pressure, Pi, and P2*" pressure at the end of pipe. The Settine of Corliss Valves. There are three marks on the hut- of the wrist-plate which indicate the extremes of throw and the centra* position accordingly as they coincide with another mark on the stand. Fix the wrist-plate in the central position, unhooking the rod connecting to the eccentric. Remove the back bonnets of the valves, and marks will be found on the valves and valve-chambers which indicate respectively the working edges of the valves and ports. ^ By means of the adjustable rods which connect the valve-arms to the wrist-plate set the steam- valves so that they will have a lap of i to i in. (the former for a 10-in. cyl., and the latter for a 35-in. cyl., — intermediate sizes in proportion). Similarly, set the exhaust-valves with tV to i in. lap for non-condensing, and with * to i in. lap for condensing engines. Adjust tne dash-pot rods by turning the wrist-plate to the extremes of travel and regulate their lengths so that when thev are down as far as they will go the steel blocks on the valve-arms will barely clear the shoulders on the hooks. (If the rods are too long they will be bent, if too short the hooks will not engage and the valves will not open.) Hook the connecting-rod to the wrist-plate, loosen the eccentric, turn t over and adjust the eccentric-rods so that the wrist-plate will have correct INERTIA DIAGRAMS. 71 extremes of travel, as shown by the marks on hub. Place the engine on either dead-center, turn the eccentric enough more than one-fourth of a revolution in advance of the crank (in the direction of rotation) to show an opening of the steam- valve (at the piston end of cylinder) of t? to ^ in., according to the speed, this being the lead. The higher the speed the more the lead required. Set the eccentric, turn to the other dead-center and obtain the same lead bv adjusting the length of the rod connecting to wrist -plate. To adjust the regulator connections to the cut-off cams, turn the wrist-plate to one extreme of travel and adjust the rod connecting to the opposite cam so that the cam will clear the steel in the tail of hook by ^ m. Turn to the other extreme of travel and adjust the other cam. To equalize the cut-off, block up the regulator about li in., which is its average position when nmning. Turn the engine slowly and note the positions of cross-head when the cut-off cams trip and the valves close. These positions should be at equal distances from the respective extremes of travel of the cross-head, and the rods should be adjusted until they are. Indicator cards should then be taken* and such readjust- ments made as are required for the equalisation of the diagrams. To Place an Engine on a Dead-center. Locate by a mark on the guides the position of a mark on the cross-head when it is at any point near the end of the outward stroke. Denote this position on the fly- wheel rim bv a mark which coincides with a fixed reference pointer. Turn the engine beyond the dead-center and on the return stroke until the mark on the cross-head coincides with that on the guides. Note this position on fly-wheel by making a mark at the reference pointer. Find the point midway between the two marks on the fly-wheel rim and turn the engine until this mid point coincides with reference pointer and the engine will be on a dead-center. To avoid the errors which might arise from looseness of bearings, the engine should be turned a little beyond the original position on tne return stroke and the motion then reversed up to the original position so that the same brasses will press on the crank- pin in both observations. Acceleration, Inertia, and Crank-effort Diagrams. The effect of the reciprocating parts of an engine is shown in Fig. 16. A vertical en^pne is chosen for illustration as both the inertia force and the dead weight of the moving mass are present, the effect of the latter being absent in a horiaontal engine. Draw the crank-circle J KLAf with radius 4 — 21 in. and the connecting-rod 3 4 = 90 in. Draw thepolar velocity curves KU and MU and also tne velocity curve AXB. These curves are con- structed as follows* In (II), if Ty moves uniformly, AW represents the crank velocity. Project the connecting-rod PW to C and AC will then be the corresponding piston velocity of the point P. Revolve ^C to AE on the line A W and rl will be a point in the polar velocity curve. Trans- fer AC to PF and F will be a point in the velocity curve JKH. The remaining points of each curve are similarly determined. The crank 4 makes 88 rev. per min., and the crank-pin consequently has a velocity of 16.1 ft. per sec. and OK (=» ordinate X) should be divided into 16.1 parts to serve as a scale of measurement. The acceleration curve, QTR must then be drawn by the method shown in (III). Let AEB (III) be the velocity curve. Draw a tangent at any point E, a normal, ED and let fall a perpendicular EC to AB. Set off CF = CD by revolving CD through 90** and F will be a point in the acceleration curve OKH. QT and TR show respectively the increase and decrease of velocity for the downward stroke and RT and TQ the acceleration and retardation for the up stroke. The force moving the reciprocating parts around the dead-centers J and L = -^5-. The inertia force, «—, whence, /, the acceleration =-^ =» on g R Tfi 1 y 1 fi 1 — "^ -g ' =148 ft. per sec. AQ, therefore, should be divided into 148 parts for a scale of acceleration in ft. per sec. The moving parts of the engine weigh 8,030 lbs. and the inertia force at any moment, F = ~«= 8 030 g^^X acceleration, or, at AQ( = 148 ft. per sec), F = 36,911 lbs. Draw NSP below QTR. each ordinate of distance between the two curves being equal to QN, which is 8,030 lbs. by scale where AQ = 36,911 lbs. NSP 72 HEAT AND THE STEAM ENGINE. is the curve of inertia pressure. The pressure per sq. in. on piston <it AQ = 36,91 1 -5- 491( « area of piston in sq. in. ) = 75.2 lbs. Draw the indicator cards to this scale, viz.: EQXHB for the top of piston and FPGA lor the bottom. When QXHB is being drawn by the indicator on the top Bide of piston, AFR is being drawn on the bottom side, and deducting the ordinates at F from those at H, the net effective pressine y'\\\ be repre- sented by the soUd hne WR. Similarly, by deducting fiordmatea from INERTIA DIAGRAMS. 73. G the curve of net pressure is shown along VN The actual total pres- sure transmitted to the crank-inn during the first half of the stroke will be less than that shown on the indicator diagram by the ainoimt re<iuired to set the reciprocating masses in motion, and during the latter half of the 8croke the indicated pressure will be increased by the backward pull needed to absorb the inertia; The top card accordingly loses the area ANS and gains SBP, the resulting pressure areas then oeing NIXWPSN for the top and PZVNSP for the bottom, or, erecting the resulting ordinates on the base AB, the top and bottom areas are respectively AbdBA and BefAB. To equalize these areas it will "be seen that the cut-ofif on the bottom diagram is considerably later than that on the top diagram, on account of the dead weight which has to be supported. Only the recipro- cating parts cause inertia force. The crank end of the connecting-rod is a rotating part, and it is customary to assume i of the weight of the rod - as reciprocating. The revolving parts are balanced by opposing weights on the crank-shaft. When the crank is on either dead-center all the pressure is received on the bearings, while at mid -stroke the pressure is exerted tangentially with no pressure on the bearings excepting that due to weight. At all other points the pressure is partly tangential and - partly normal. The tangential pressure at any point is proportionally repre.sented by the corresponding radius vector of the curve KU. If JO is then divided into tenths the length of each radius vector in terms of these divisions will represent its virtual crank-arm in relation to the pres- sures transmitted along ABO. Multiply each net pressure ordinate along AB by its virtual crank-arm and set off the resulting tangential crank pressures radially, with the crank-circle JKLM. as a oase Une and the curves of crank-effort, JghjL and LklmJ will be obtained. These curves ' may be set out on a straight base by stepping JK out on CO, and KL on OD and then transferring the radial ordinates to vertical positions ; along the line CD when the curves CnD and DpC result. In locomotives two cranks at right angles are employed and in marine engines three cranks, 120° apart. A combination diagram may be made bv superposing the diagrams of the individual cranks and adding the radial ordinates. (The foregoing discussion is taken from Lineham's Text-Book of Mech. Eng.) Calculation of Fly-Wheels. On the base line EH (Fig. 17) lay out a series of crank-eflfort diagrams, making EAF and FCG equal to DpC and CnD of Fig. 16. ^G=l. rev.=3i;r=ll ft. The mean ordinates of EAF and FCD are 29,500 lbs. and 25,000 lbs. respectively and one-half their sum, or 27,250 lbs., is the mean effort for the continuous diagram. Draw JK at this pressure above EH. The areas A^ C, etc., above the Fig. 17. line JK show surplus work, while J9, Z>, etc., below the line show deficits. The fly-wheel must absorb the work of A, C, etc., and give it out again at B, Z), etc., thus tending to equalize the crank-effort. The mean pres- sures and distances are measured at A, B, C, and D and are shown by the work rectangles, and ^ +C = B + Z) = 88,700 ft.-lbs. The greatest rectangle is D, =49,560 ft.-lbs., which is the amount of energy the fly- wheel must be able to deliver and thereby decrease its velocity. The heavier the \<rheel the smaller will be its fluctuation of velocity. Let t>=- mean velocity in ft. per sec. and let the total fluctuation of velocity =-r-t where k varies from 20 to 300, according to the steadiness required. Let Vi and V2 he the maximum and minimum velocities at the mean radius. 74 HSJLT AND THE STEAM ENGINE. ^=the energy area (in this case 49,560 ft.-lbs.). Then ■ *^-"' •■°^. where to—weight of wheel in lbs. Now, t>i — t>2=-r' '^+t'2='2t>, and v2xRN-i-G0t where i2 = radius of gyration of wheel in feet. Substituting and reducing, wei^t of wheel in lbs. w— *t,2jj2 • Values of k (r""^ Per- centage of fluctuation from the mean speed). For hammering and crushing machinery. ib = 5; for pumping and shear- ing machinery, 20 to 30; for ordinary driving engines for machine-shops, 30 to 35; for milling machinery and gear transmission, 50; for spinning machinery, 50 to 100; for electric hghting, 150 to 300. If the diameter of the wheel be large and the rim heavy (as compared with the arms and hub), R may be taken as the radius to center of lim section. If the hub and arms are of considerable weight, assume a section of fly-wheel, replacing the arms by a thin disc of equal weight and treat the whole cross-section of the wheel through the shaft as a beam section, finding its modulus, S, multiplsong the same by y, the outer radius of wheel, and thus obtaining /, which, divided by the total area of cross- section, will give B^. v must be measured at R and great care taken to avoid the confusion incidental to calculating in both feet and inches. w =» 7^2 V2 * ^^®^ ^* '* '^^ ^ '^^ diam. of cyl. in in., stroke in in., and diam. of fly-wheel in feet, respectively (J. B. Stanwood). Values of C: ordinary slide- vaive engines, 350,000; Corliss engine for ordinary duty and slide-valve engines for electric lighting, 700,000; automatic high- speed and (Corliss engines for electric lighting, 1,000,000. Proportions of Steam-Engrine Parts. In the following table the formulas attributed to Prof. John H. Barr are mean results obtained by him from some 160 engines (from 12 American builders) ranging from 20 to 750 H.P. Those of J. B. Stanwood are the conclusions of an extended practice and those of Wm. Kent are the best probable mean expressions of a large number of formulas considered and discussed by him in The Mechanical Engineer's Pocket Book. The following notation is employed - o==area of piston, Z= length of stroke, d=diam. of piston, (fi«=diam. of fly-wheel, «— diam. of cylinder studs, < = thickness, 2i= length of con- necting-rod (2.5/ to 30' All in inch measure. N — T.p.m., p=inBX. steam pressure in lbs. per aa. in., F—piston velocity in ft. per min., H.P. and I.H.P. = rated and indicated horse-power, respectively. (See also related matter in Strength of Materials, ante.) Barr. Kent. Stanwood. Cylinder: Thickness of walls, 0.05^-1-0.5 m. 0.0004^p -1-0.3 in. " *• flanges, 1.2 X above ** heads. " " 0.00036dp-|-0.31 in. Studs. No. of (6). 0.7d 0.0002d2p-4-»2 diam., 0.025d -I- 0.5 in. 0.01414 Vp^^ Len^ofptaton. 0.46d(h^)j ^ Piston-rod diam, 0.32d(l.s.) : HSghsp^d, 0.145^1 „„,3^^ 0.1«to0.17«» Connecting-rods : High speed, rectan- g u 1 a r section, thickness, <- 0.05r^Zjd O.OlrfV^+0.6 in. Mean height- 2.7< (Crank end, 2.25^ cross-head end, 1.50 Low speed, circular section, mean diam.- 0.092>/w 0.021dV^ STEAM-ENGINE PROPORTIONS. 75 Barr. Cross-head pins: ( L » length, i> »diam.) High speed, LD = 0.08a ; ^ = 1.25 Low •• LD-0.07a; §-13 Crank-pins: (L — length, 2>— diam.) High speed. L2>- 0.24a; L- ^'^^'^ - +2.5 in. Low •• LD-0.09o;L = ^^^j^+2m. Crank-shafts, Main Journals: High speed, \LD - 0.46o ; D - 7.W^^' ; L - 2.2D j Low •• (LZ>-0.56a; i>-6.84/^*; L-1.9Z>j Steam-ports, area: Slide-valve. High speed, aV+S.SOO Corliss, 01^+6,800 Exhaust-ports, area: Slide-valve, High speed, ay+ 5,500 Corliss. aV-i- 5,500 Steam pipes, area: Slide-valve, diam.= Highspeed, aV-i- 6,500 Corliss. aF-4- 6,000 Exhaust-pipes, area: Slide-valve, diam.- Hi«h speed, 01^-5-4,400 Corliss, ay-4-3,800 Fly-wheel weight, in lbs. per H.P. : Slide-valve, Hi«h speed. 1, 200.000,000,000 -4-<2i>iVS Corliss, Weight of engine: Slide-valve, High speed, 115 lbs. per I.H.P. Corliss. 175 •• •• •• Stanwood. [ L-0.25dto0.3<l [ Z)-0.18dto0.2d L=0.25dto0.34 D-0.22dto0.27d L-0.85dtod JD-0.42dto0.5d 0.08a to 0.09a 0.1a to 0.12a 0.07a to 0.08a 0.15a to 0.2a 0.18a to 0.22a 0.10a to 0.12a 0.25d-l-0.5in. 0.33d 0.3d 0.33d 0.376d 0.33d to 0.37d 33 25 to 33 80 to 120 lbs. per H.P. 125 to 135 90 to 120 220 to 250 Piston speed in ft. per min. — 600; weight of reciprocating parts in lbs.. for high-speed engines — 1.860 .OOOd^-^-ZiV^; square feet of belt surface per I.H.P. per min. — 55 (high speed) and 35 (low speed) (Barr). Clearance space: Corliss, 0.022 to 0.042; high speed, double valve, 0.032 to 0.052; high speed, single valve, 0.082 to 0.152; slide-valve, 0.062 to 0.082. Pressures on wearing surfaces in lbs. (L— length, D — diam., both in in.): Main bearings, 140LZ> to 160 LD\ crank-pins, 1,OOOLD to 1,200LD; cross-head pins, 1,200LD to 1,600L£> (Stanwood). Pressure on thrust-bearings— 35 to 40 lbs. per sq. in. of area (Fowler). Receiver volume for compound engine: It the cylinders are tandem, the connecting Pteam passages will be sufficient. If the cranks are at 90**, the volume of receiver should be at least as great as that of the low-pres- sure cylinder. 76 HEAT AND THE STEAM ENGINE. TEMPERATITBE-ENtBOPYi DIAGRAMS. In an indicator diagram the co-ordinates are pressure and volume and the area represents work done per stroke, in ft.-lbs. In a temperature-entropy diagram the vertical ordinates are absolute temperatures, the horizontal ordinates, or abscissas, are quantities termed entropy, and the area represents energy measured in heat-imits. Entropy, therefore, is length in a diagram whose area represents energy in heiat- units and whose height is absolute temperature. Isothermals on this diagram are horizontal straight hnes, — the tem- perature being constant, — and adiabatics are vertical straight hnes, — there being no change in the quantity of heat during a change of temperature. Application to Carnot Cycle (Fig. 18). Heat supplied at ri» area Hi, and heat rejected at t2»> area H2, AB and CD being isothermals and BC and AD being adiabatics. Work done = Hi — H2, and efficiency =» Construction of Diagram for Tirater and Steam. The diagram is drawn to represent the changes of 1 lb. of working substance and an arbitrary zero point is chosen to work from (i.e., 32° F. or 482? absolute). The entropy of water, then, at 492* = 0. At any other absolute temperature, t, the entropy Fifi:. 18. of water, ^ — loger— loge 492» * logeT-6.198. The additional entropy due to the conversion of water into steam is FrAbB. / M 300 200 100 32 ■•^ equal to tlte latent heat (or heat necessary to convert the water into steam) TEMPERATURE-ENTROPY DIAGRAMS. 77 divided by the corresponding absolute temperature, or L-7-t = ^ . following table gives tne * The Entropy per Lb. Weight. t T Water from 32° F. (^^). Steam (^^). Steam and Water(^,^+^^). 32 492 0.0000 2.2189 2.2189 50 510 .0359 2.1163 2.1522 100 560 .1296 1.8649 1.9945 150 610 .2154 1.6547 1.8701 200 660 .2949 1.476 1.7709 250 710 .3690 1.322 1.691 300 760 .4386 1.188 1.6266 350 810 .5042 1.0698 1.574 400 860 .5665 0.9649 1.5314 The results in this table are plotted in Fig. 19, ON being the water line or the plotting of the values of 6u}, and MP the dry-steam line, or tfnp+^a- If 1 lb. of water is raised from 32° F. to n, the heat units required will be represented by the area Chi A. The heat then required to convert the water into steam will be the area nBCAn The entropy of the water will be OA as measured by the scale, that of the latent heat by AC, and the entropy of the steam and water by OC(=OA+AC). From steam-tables it is found that 1 lb. of dry saturated steam at 334° F. (794° ab.) occupies 4 cu. ft. If the isothermal at this temperature be divided into four equal parts, each part will represent 1 cubic foot. Also ah may be divided into eight parts, each representing 1 cu. ft. (1 lb. = 8 cu. It. at 284° F.). Other isothermals may be similarly divided, and if all of the points for say 1 cu. ft. are connected, the resulting curve wiU be a curve of constant volume (for 1 cu. ft.). If 1 lb. of water at 334° F. be supplied with heat sufficient to evaporate one-quarter of itself, the distance dA will represent the portion of the total Fig.20, M.£.P.^ 34.56 Ite. lOi \12 I I I I heat de required for the whole lb. The dryness of the steam (i of it being evaporated) will then be 0.25, and it may be stated that. The dryness is represented in the entropy diagram by the fraction (hor. dist. of point from water Une)-J-(hor. dist. bet. steam and water lines) »=di^-^de in the instance under coDsideration. 78 HEAT AND THE STEAM ENGINE. If the steam is superheated to va before caitering the oyUnder, the addi- ional entropy, C ' ' ' ' ' 0.48(logeTa-logeri] CL, to Ti2 _ _ - - - , - obtained from the formula: Entropy, CL = To Draw the Entropy Diagram from the Data in an Indicator Diaeram.. — Fis. 20 is the indicator diagram of an engine having the follow- ing data: Initial pressure. 105 lbs., back-pressure, 17 lbs. (both absolute); ^— 0.5t Fig.2U r.p.m. = 90; cylinder. 14X36; m.e.p. =34.56 lbs.; I.H.P.- 87.06; area of cyl. = 153.94 sq. in.; volume of cyl. = 3.207 eu. ft.; volume of clearance (3.448%) = 0.11058 cu. ft.; lbs. steam used per hour=-2,133.5 («-24.5 lbs. per I.H.P. hr.); lbs. of entering steam per stroke =0.197547. The compression steam is generally assumed to be dry, and, at point 17 (where vol. =0.16587 cu. ft. and pressure — 60 lb.), its weight will be — 0.16587 X 0.14236 (or the weight of 1 cu. ft. at 60 lbs.) = 0.023613 lb. .'. Total steam in cyl. = 0.197547 +0.023613 = 0.221 16 lb. and the vol of 1 lb. of steam similar to that in the cylinder, x = actual vol. in cyl. +0.22116. The pressures and values of x for the various points of Fig. 20 may now be plotted on Fig 21. For example, the pressure at point 7 on the iudicator diagram is 40 lbs. (absolute). The contenta (^ oyL at this TBMPBEATUBE-ENTBOPT DIAOBAHS. 79 lioint are 1.7694 cu. ft., which, divided by 0.22116, gives the volume x. of 1 lb., or 8 cu. ft. and point 7 on the entropy diagram is thus located by the intersection of the constant- volume curve 8 and the horizontal line of temperature 267* F. (727" abs.). which corre- sponds to a pressure of 40 lbs. absolute. Losses. The entropy diagram just con- sidered may be compared with that of the Hankine cycle for an ideal engine where the expansion is adiabatic down to back-pressure and where there is no compression. This latter diagram is the area ABCDA, BC being drawn at 108 lbs. (assumini| a drop of 3 lbs. from the separator to cylinder). The loss BE4GCB is that due to wire- drawing during the entrance of the steam; loss 4(?i/64 occurs during expansion and is due to condensation, leakage, etc.; loss JK12J is due to incomplete expansion; loss 13^.^1 16 13 is due to clearance, com- pression, etc. All areas represent heat-units according to scale. The area 4LMN4 represents additional Uquefaction loss after cut-oflF, and 7NKJ7 the gain due to re- evaporation. Fig. 21 shows only the work- ing part of diagram, the full diagram on a smaller scale being shown by Fig. 21a. Entropy Diagrams Applied to Inter- nal Combustion Engines. ^^H-t-r; d4>~dH+r. dH^kvdz + (AP-i-J)dV, and iAP+J)'^(kp—kv)T-hV,OT, combining these equations, <Mr-s-T = d^ = (A;tjdT -!-t) + (Ap — At;)dF -i- F, which is the general equation for change of entropy. (A »» numerical constant, y — Joule's equivalent = 778, P = lbs. pressure per sq.ft.) Integrating between limits, ^i— ^— ib loge (ri-i-ra) when the volume is constant, and ^i— ^=A;plog« (11+72) when the pressure is con- stant. When P and V vary according to the law PF*-= constant, considering that PV'^Rz, letting kp-i-kv^rf substituting in the general equation and reducing, ^— ^ — *»— ^jlogc — , or, the change in entropy whenPV* — constant. In adiabatic expansion r—x, hence ^— ^=^0. ^ r In the theoretical gas-engine diagram (Fig. 22, I.) Pb—PaVa -f-Vft , and xb='PbVb-t-(Kp--Kv), where V6 = specific volume of explosive mixture at b, ^Tpand ^Tv « RDecific heats of mixture in ft.-lbs. ( — ibp and kv multiplied by 778, or the equivalent of 1 heat-unit in ft.-lbs. In the following calcu- lations the old value, — 772, — has been employed). If tb is known, t6 — Ta(r)''~*. where r^Va-^Vb and r='kp+kv. Tc«=T&Pe-+-P6. The increase of entropy during tne explosion is represented by the logarithmic curve be (II, Fi^. 22) and increase of entropv from b to e-' Ac— ^b'^kv loge (re +Tb). Adiabatic expansion is shown oy the vertical line cd, there being no change in the aiaount of entropy. rd^PdVd-*- CKp-Kv) and Pd~P.Vcr'i-Vdr = PcVi>r+Var. From d to a (exhaust at const, vol.), <^ — ^a'^kvloge{rd-t-Ta), which is negative. The exhaust and suction strokes do not enter into considera- tion, the temperature being assumed as constant. The diagram is completed by drawing OX at the absolute sero of tem- perature, when the work done per cycles area abed; heat received per cycle = area ObcX; thermal efficiency = abed -i-ObcX; heat rejected into exhaust = area OadX. Since (^e— ^) = (^ — ^a) and 6c is governed by the same law as ad, the ratio of the two temperatures is constant and dependent only on the amount of compression, a high ratio resulting in a correspondingly increased efficiency. The indicator card of a Orossley Otto engine tested by Prof, Ci4>per Fig. 21a. 80 HEAT AND THE STEAM ENGINE. is shown in III, Fig. 22, the data for and a more complete analysis of which may be found in Golding'a "Theta Phi Diagrams.'' (^linder, 8.5 in. diam. by 18 in. stroke, vol.— 0.591 cu. ft., clearance vol. =0.2467 cu. ft., total vol. =0.8377 cu. ft. R.p.m.-- 162.5, explosions per min. = 71.2, net I.H.P. = 13.32. Gas used per hour = 279.75 cu. ft., gas per explosion =0.06544 cu. ft. at 518° F. and 14.8 lbs. pressure, abso- c K W b N^ V 1 K. 1 V, I Fig.22. lute (=» 0.0822 cu. ft. at temperature and pressure at a, or 605° and 13.8 lbs.) Pressures in lbs. per sq. in. at a, 6, c, d and c=13.8, 07.8, 240, 240 and 48.71, respectively. Volumes in cu. ft. at same points =0.8377, 0.2467, 0.2467, 0.2617 and 0.8377, respectively. Since VaV/ - PbVb\ from the above values of p and V, x= 1.3707 for the ideal extiansion curve == 1.3022 'or the compression curve (both dotted). The location of e is found bj' TEMPERATURE-ENTROPY DIAGRAMS. 81 producing the actual expansion curve until it intersects the vertical ae. The coal gas (London) used had the following percentages by weight: CH4, 42.79; C2ri4 and C4H8, 18.21; H, 8.69; CO, 18.33; N, 7.14; CO2 and O, 4.84. 1 cu. ft. =0.0329 lb. A;t' =0.5279, jfcp=0.6961. The prod- ucts of combust on or exhaust gases had the following composition (by weight): CO2. 10.17; O, 6.7; N, 83.18. A;tJ = 0.1716, Ap =0.2385, 1 cu. ft.= 0.082 lb. The clearance (filled with exhaust gases) held 0.2467X0.082 = 0.02023 lb. at 492<» and 14.7 lbs., or, [(0.02023 X 4^,2X14.8) -5- (605 X 14.7)1=0.01656 lb. at 605® and 14.8 lbs. pressure at the beginning of suction stroke. The gas (0.06544 cu. ft.) having a specific volume of 34.87 cu. ft. per lb. at atmospheric pressure and temperature weighed 0.001877 lb. (Vol. at 605<» and 14.8 lb. =0.0822 cu. ft.) Air per explosion =0.8377 - (0.2467 +0.0822) =0.5088 cu. ft., which, at 606*> and 13.8 lbs. pressure at a weighed 0.03131 lb. (16.25 cu. ft. per lb.). Total weight of mixture = 0.049747 lb. Specific heats of mixture /rt;= 141.43 ft.-lbs., iiCp = 199.09 ft.-lbs., Kp~Kv = ^7.m ft.-lbs., A;p=0.25788, A:u = 0.1832, r = 1.4077. From these values and the previously given temperature equations, 76 = 840° F. (absolute), tc = 2,973'', 7^ = 3,154°, Te = 2,048°, and t« = 580°. (This is 25<» lower than the value assumed, 605°, but the difference need not be con- sidered.) Taking entropy at & as zero, the entropy at c=4>c — 4>b = Tcv\oge (tc-<-t6) = 0.23158. 4>d-<tic=kp loge (T<i-^Tc) =0.25788 Xlogc(3,154 -r- 2,973) = 0.01624. ^e - ^d = fcv^^ loge(Trf -i-«) = 0.1832[( 1.3707 - 1 .4077) -J- 0.3707] loge(3,154 -J- 2,048) =0.00709. ^a-^e = A;vloge {xe-^za)= -0.23112. <t>b-<l>a'^kv'~'[ loge (t6-5-t«)=- 0.02369. Positive entropy, h to e = 0.23 158 -I- 0.01 524-1- 0.00709=0.25472. Negative entropy, e to 6 = 0.23112-1-0.02369=0.25481. The two sums should exactly balaiice, the slight difference being due to insufficiently extended calculations. The diagram for the ideal cycle is represented by abcdea (IV, Fig, 22), whose area = 171.875 B.T.U. or the work performed by 1 lb. of the mix- ture. The work per explosion (i.e., of 0.049747 lb.) = 8.55 B.T.U. =6,600 ft.-lbs. The actual cycle is now to be considered. The curves he and cd in the entropy diagram are correct, but during expansion the actual curve of pressures differs considerably from the ideal or dotted curve, and it is therefore necessary to select several points on the actual curve and calculate the temperature and entropy at each. These values are given in the fol- lowing table ; p dSS"^. ^q^.'iJf.^ inCu.*Ft. inDJis. F. x. Entropy (^). d 240 .2617 3,154 , ooAr; .24682 g 170 .335 2.858 1 5fiK« .24734 X 134 .394 2,650 1 47^ -24559 i 109 .453 2,478 i SoS? .24374 % 80.5 .572 2,312 1 Q^ofi -24837 I 62.5 .6897 2,164 i.do^o .25027 m 63.8 .749 2,023 .24404 n 38 .808 1,541 .200 o 24 .8377 1,009 .1217 At m, just after release, p = 53.8 lb.; the pressure at / on ideal curve (vertically above m, — ^at same vol.) = 56.79 lb. ; Tm = Pmym-^{Kp—Kv)X 0.049747 = (53.8 X 144) X 0.749 -^ (57.66 X 0.049747) = 2,023°; t/= 2,135°. The drop of entropy from 2,135° to 2,023° =0.1832 log« (2,135-5-2,023) = 0.00991, which must be subtracted from the entropy at /. The entropy at / in excess of that at d=A:v^—^^oS«(Trf-^T/) = 0.00713, consequently the entropy at m= entropy at d-H additional entropy to / -drop in entropy from / to m =0.24682 + 0.00713 --0.00991 =0.24404. Values for points n and o are similarly obtained, the results being included jn above table. 82 HEAT AND THE STEAM ENGINE. The heat transformed into work « area abcdjloa. This, however, does not represent the total heat generated during the explosion. The total avail- able heat of each explosion = 36.04 B.T.U. (or that of 0.001877 lb. of gas. whose calorific value is 19,200 B.T.U. per lb.). To represent this on the diagram, produce 6o to p so that the area 6i6ppi = 36.04+ 0.049747 — 724.5 B.T.U. per lb. of mixture. Tp==T6+Tr (Tr=the rise in temperature from b due to complete combustion), rr — 724.5 -J- ifev = 3,966° and tp = 3,966 + 840-4,795°. Net heat transformed into work -«6cd;7o- 8.2 B.T.U. per explosion, or 22.75% of the total available heat. Heat given to cylinder walls during compression stroke =aia&6i— 0.77 B.T.U Heat given to exhaust — aioom/Zi — 13.63 B.T.U, Tm remainder (liljdcppi^ 13.44 B.T.U.) is transmitted through the cylinder walls, and the total heat passing through walls — 13.44+0.77 — 14.21 B.T.U. —heat given to i'acket water plus that radiated from the exterior surface of cylinder lead and piston. In an ideal engine (iwe., one with a non-conducting cylinder, complete combustion, esdutuat at constant voliune, adiabatic expansion and com- pression) the work per explosion = area H>pq, and the maximum possible work— 100 (t6— T„)-i-Tft per cent of the total heat evolved,- 100(840 — 580) -J- 840-30.95% of the 36.04 B.T.U. = 11.154 B.T.U. oer explosion. The net work actually obtained = 8.2 B.T.U. — 73.5% of tne maximum. The same general method is employed for oil engines, temperatures being calculated from PV^Rr, etc. In a Diesel engine where oil is sprayed into the cylinder under air pressure for 5 to 10% of the combustion stroke. A:p -0.264 (mean value) and if r is taken at 1.408. A;i; =0.1875. STEAM TURBINES. Turbines are machines in which a rotary motion is obtained by means of the gradual change of the momentum of a fluid. In steam turbines the energy given out by steam during its expansion from admission to exhaust pressure is transformed into mechanical work, either by means of pressure or of the velocity of the steam while expanding. The De Laval turbine is one of pure impact and consists of a wheel carrying a row of radially attached vanes or buckets. The steam is delivered to these vanes from stationary nozzles, in which it is fully expanded (thus attaining the highest practicable velocity) and after passing the vanes is exhausted either into the atmosphere or into a condenser. The nozzles are inclined to the plane of the wheel at an angle of 20°; the inlet and outlet angles of the vanes range from 32° to 36° according to the size of the turbine. The best peripheral velocity is about 47% of the steam velocity. Economical reasons restrict it to about 1,400 ft. per sec. for large wheels and 500 fU per sec. for small ones. R.p.m. of wheels range from 10,000 to 30,000, and are reduced to 0.1 these values by helical gears. In the Parsons turbine a drum with rows of radial vanes revolves in a stationary case. Between each row of moving vanes there is a ring of vanes fixed to the case which deflects the direction of the steam flow to the next rotating row of vanes. The diameters of drum and casing increase in stens from inlet to exhaust end, the steam flowing through the vanes in the annular space between the drum and case. The expansion is prac- ^ic&,llv fl.di&D&'tic Tiie Rateau mu/ticellular turbine in effect consists of a number of wheels of tne De Laval tj^Je mounted side by side on the same shaft, each wheel rotating in a compartment of its own and the exhaust of each wheel being led through nozzles or openings in the partition walls to the next succeed- ing wheel. Step-by-step expansion and moderate speeds are thereby obtained. In the Curtis turbine the nozzles deliver steam at a velocity of about 2,000 ft. per sec. and this velocity is absorbed by a series of moving vane wheels on a vertical shaft with alternating fixed rings of stationary guide bla'fes. similar to Parsons* arrangement. When the initial velocity has been absorbed the steam is again expanded throuflfh another set of nozzles to a further series of wheels, and so on. By this comooundinat the nerioheral speed is kept down around 400 ft. per sec. In the following table the pressures are gauge pressures. STEAM TURBINES. 83 Steam Turbine Data. Steam q,,*^, Lbs. Steam per Hour. IbJu. sue. V«suum.Pres-R.P.M.|»P»f-0.6 F„U Load, sure. Lioad. in. lb. ° F. Parsons. 400 K.W. 25 125 3.300 15.41 per B.H.P. 1,260 •* 25 150 1,200 14.4 1,260 •* 28 150 1,200 77 13.2 De Laval. 30 H.P 100 2,000 41 40 30 •* 50 2,000 50 50 30 ** 25.6 125 2,000 25-30 22 300 •* 27 200 900 20-90 16.5 14.5 300 " 27 200 900 17.5 15.5 Curtis. 2,000 K.W 28.8 160 750 242 16.3 15.3 R&teau 500 HP (1.33 J) 62 2,400 18 E.H.P. B.H.P K.W. E.H.P. 500 *' (1.63:^) 121 2,400 15.8 500 •• 29 180 2,400 90 11.5 Westinghouse- Parsons. 600 " 28 150 100 14.34 12.48 *' B.H.P. 600 " 28 150 15.8613.89 Flow of Steam through Nozzles. Zeuner's formula for the velocity of steam flowing through a nozzle and expanding adiabatically may be simplified to the followi ng form with out involving appreciate emor: V (in ft. per 8ec.)=224V'A--AH-Z«--Zi«i (1), wfaeie h and Ai aie the initial and final heat in the water in B.T.U.. / and h the initial and final latent heat in the steam in B.T.U., and • and Si are the initial and final degrees of flatoration of the steam. 9i'=>a — {t^ti){c—t)x'10~'^ (2), where «i=saturation after adiabatic expansion, 8 = initial saturation, t and ^i are temperatures (F '^) before and after expansion. Vcdues of c and x. (a is assumed or ascertained beforehand.) Whens »= 1 .95 .90 .85 .80 .75 ^ .70 c=» 900 870 845 833 817 770 710 a;=» 16.6 15.7 14.7 13.4 12 11.5 11 The weight of steam delivered per sq. in. of nozzle cross-section per minute in lbs., tt;=0.417v-J-«tt (3), where t«— cu. ft. in 1 lb. of dry steam at the pressure corresponding to v. At that section of the nozzle where the pressure has dropped to 58% of the initial pressure the flow per sq. in. is greatest, hence this section is the smallest and the nozzle diverges from this point to the mouth. The theoretical minimimi weight of steam per H.P. hour, W= 127,000,000 -i-v^ (at mouth) (4). (The foregoing matter has been derived from an article by A. M. Levin in Am. Mach., 6-30-04.) Example — Steam at 185 lbs. (absolute) containing 20% \>{ moistiu^ (a=O.S) is required to expand adiabatically in a nozzle to 1 lb. (absolute). p at throat = 185X0.58 = 107.3 lbs. From formula (2) and steam-tables the following values are found p. lbs. <•». I. «. u. h. Initial. . . . Throat. . . . Mouth. . . . ... 185 ... 107.3 1 375 333 102 848 879 1,043 0.800 .778 .655 2.45 4.08 334 348 304 70 Substituting in (1) and (3), v at throat = 1,391 ft. per sec, v at mouth = 3,703 ft. per sec, w at throat = 182.75 lbs. per sq. in. per min., and w at mouth =7.058 lbs. per sq. in. per min. Area of cross-section at mouth = (182.75-*-7.058 = 25.9)Xsection at throats Min. wt. of steam per H.P. hour (from (4)) = 9.27 lbs. The kinetic energy of 1 lb. 8team = t;2^.2^; if t) = 3,703, kinetic energy = 213,200 ft.-lbs. In designing a nozzle, calculate v at mouth from the conditions assumed — then i;2(mouth)-«-29= kinetic energy of 1 lb. of steam in ft.-lbs. Assume 84 HEAT AND THE STEAM ENGINE. this energy to develop from at the inlet to its full value at the mouth by eguail increments per incremeq^ of nozzle length, and plot curve of velocities corresponding thereto. Assume several pre^ures between supply and moutn and find the corresponding velocities from (1), locating these pressures vertically under the corresponding velocities on the ciuye, and draw a second or pressure-curve through these points. Determine «, h. I, and u from steam-tables and formula (2) and find values of to by formula (3) for the various pressures chosen. The reciprocals of w will be the sq. in. of cross-section per lb. of steam per min., which, if plotted, will give points in the curve of nozzle cross-section. (For an elaboration of this subject, consult Stodola's *'The Steam Tur- bine," translated by Dr. L. C. Loewenstein, D. Van Nostrand Co.) LOCOMOTIVES. (V+ 12\ V^ g -J -h Wqq (European practice, Fowler's Pocket Book); i2i = 3-»-^ (Baldwin Loco. Wks.); fii = 4 + 0.005Fa+ o (0.28+0.03iV)^ (Wellington); Ri = ^ + J^ (Wellington, for any load- ing, 5 to 35 mi. per hr. ) ; /2i = 3 + m86V+ (^ + 1 .036) y^ (Von Borries). In these formulas -Ri « resistance in lbs. per ton of 2,000 lbs. (2,240 lbs. for first formula), V= speed in miles per hour, iV^— number of cars in train, TF"^ weight of train in tons of 2,000 lbs., and w — wt. of one car in tons. Resistance diie to grade in lbs. per ton (2,000 lbs.), Ri'=0,37S8G, where (t = grade in feet per mile. Curve resistance, in lbs. per ton, ^3 = 0.5682A, where A = angle of curvp in decrees. (The angle of a railway curve is the angle at the center pn^^- tended by a chord of 100 ft. The radius of a curve of A degreep - 5,729.65 ft. -5- A. ^ Acceleration resistance (due to change of speed), R4 = 0.0132(yi2— V^) where Vi is the higher speed. Total resistance, R^Ri + Rz+Rs+Ra. Horse-Power = ( WVR X 5,280) -»- (33,000 X 60) =0.002666W^FK. Tractive Power cannot exceed the adhesion, which varies from 20% of the weight on the drivers when rails are wet or frosty, to 22.5% when dry. At starting 25% may be attained by the use of sand. Tractive power = d^pi8 -^ d^, where d and di are respectively the diams. of cyUnder and drivers in m., pi the mean effective pressure in lbs. per sq. in., and «= stroke in in. M.E.P. = boiler pressure pXc (approx.). Values of c: Cut-off = . .iilififl c = 0.2 0.4 0.55 0.67 0.79 0.89 0.98 1 The average m.e.p. decreases as the piston speed increa'^es, as shown in the following from Bulletin No. 1, Am. Ry. Eng. & Maintenance of Way Assn.: Piston speed (ft. per min.). 250 300 400 500 600 800 1,000 1,200 M.E.P. (%) 85 80.2 70.8 62 54 40.7 31.6 26 For compound engines of the Vauclain 4-cyl. type, Tractive power in lbs. — p8(2.^D'^+d^)-i-4tdi, where p = boiler pressure, and £> = diam. of high- pressure cyl. (For a 2-cyl. or cross-compound, omit d^ from formula.) The tractive power decreases as the speed increases, as shown by the following table, where r = stroke -^diam. of driver, and a speed of 10 mi per hr. is taken as imity. F- 10 (r- 0.429). . 1 (r- 0.636). . 1 15 20 25 30 .88 .75 .64 .53 .83 .67 .64 .45 LOCOMOTIVES. 86 Weisht of Train in tons, for average freight work (including engine and tender) W « tractive power-*- [6 + 20 X (grade in per cent)]. The weight of freight carried may be taken as (PF— wt. of loco.)-*- 2. H. P. «= Tractive power XK-^ 375. Grate Area in sq. it.=^d^s-i-C (d and « in in.). For express locomotives, simple, C = 197 to 288 (average practice = 240) : compound, C— 118. For freight locomotives, simple, C = 260 to 290 (—600 for very heavy locos.); compound, C = 132 to 197 ( = 177 for good practice). (For compound locos. <f =diam. of h. p. cyl.) Heating: Surf ace = Grate areaXC. For passenger locomotives, C=» 47 to 75 (=70 for good practice). For freight locos., C = 65 to 100 (best practice on heavy locos., C = 78 to 90). Diameters of Cylinders* d = 0.642 Vdju? -*- pa, where w— weight on drivers in lbs. For the diam. of h. p. cyl. in a compound engine replace 0.542 in fonnula by 0.4 to 0.46. Diam. of 1. p. cyl. = (1.56 to 1.72) X diam. h. p. cyl. Areas of Steam-Ports. For simple locos., A =7.5% of cyl. area. For heavy, modem freight locos., A = 10% of area of h. p. cyl. and 4.6 to 6.5% of 1. p. cyl. area. Areas of Exliaust-Ports, simple, about 2.5 X area of steam-port. Piston-Tatves. Diam. of valve = 0.4 X cyl. diam. Coal Consumption. From 120 to 200 lbs. per hom: per sq. ft. of grate Under favorable conditions one I.H.P. requires the combustion of 4 to 5 lbs. of coal per hour. Balancing. To avoid oscillations the forces and couples in a horizontal plane due to the inertia of the reciprocating parts must be eliminated as far aspossible. Let ly -"Combined weight of crank-pin, connecting-rod, cross-head, piston-rod and piston -hone-half the weight of one crank-arm. (In the case of an inside cyl. take the weight of one web in place of ^ 'j ; r= radius of crank: A = radius of c. of g. of balance- weight ; a — distance between centers of wheels (i.e., c. to c. of rails); &= distance between cente rs of cyls. Then, tne weight of each balance- weight, Wf^ —^V ^ o t aiid tah 6^^-r-r, where tf=angle between radius to c. of g. aa 2 a+b of balance-weight from wheel center, and the center line of the near crank produced. For inside cyls. both balance-weights fall within the quadrant bounded by the produced center lines of the cranks. For outside cyls. tan is negative and the balance- weights are outside of the said quadrant. In the U. S. the balance-weights are equally divided between the wheels coupled together; in England they are concentrated on the drivers. The U. 8. method reduces the hammer-blow on the rails, and to still further lessen this, some builders balance only 75% of the reciprocating weight. Another rule is as follows: On the main drivers place a weight equal to one-half the weight of the back end of the connecting-rod plus one- half the weight of the front end of connecting-rod, piston, piston-rod, and cross-head. On the coupled wheels place a weight equal to one-half the weight of the parallel-rod plus one-half the weights of the front end of the main-rod, piston, piston-rod, and cross-head. Balance- weights to be opposite the crank-pins and their centers of gravity must be at the same distances from the axles as the crank-pins. Friction of I^ocomotives. An 8-wheel Schenectady passenger loco- motive tested by Prof. W. F. M. Goss gave the following results. (Cyl. 17X24, drivers, 63 in., wt., 85,000 lbs.) Cut-off at i stroke, friction at 15 mi. per hr. «= 12% of total power. «* "f " - - 55 " " •• =23% •* *• •• ••* •• *• " 15 = 7.4%*' •• «• •• X •• •• •• 55 •* •• ** ^157^ •* •• •• 86 HEAT AND THE STEAM ENGINE. STEAM-BOILERS. 87 STEAM-BOILEBS. Hopse-Power, The capacity of a boiler is fully expressed by stating the quantity of water it is capable of evaporating in a given time under given conditions, and the H.P. of the steam so generated depends entirely on the economy of the engine in which it is used. There is, however, a commercial demand for rating boilers in terms of H.P. and the A.S.M.E. committee has reconmiended the following: The unit of commercial H.P. developed by a boiler shall be 34.5 lbs. of water evaporated per hour from a feed- water temperature of 212° F. into dry steam of the same tempera- ture, -hich is equivjJent to 33,317 B.T.U. per hour and also practically equivalent to an evaporation of 30 lbs. of water from 100° F. into steam at 70 lbs. gauge pressure. Heating Surface is all that siuiace which is surrounded on one side by water to be heated and on the other by flame or heated gases. Heating surface in sq. ft., A^^cQ-i-H, where Q — quantity of water evap- orated per hour, H—totsd heat of the steam at boiler pressure, and c for locomotive boilers = 90, for Scotch marine boilers » 180, for Cornish — 220, for plain cyUnder — 280, for return-tubular and water-tube boilers = 400. Relative Values of Heating Surfaces per sq. ft. compared with flat plates Flat plate above fire, 1; cylindrical surface above and concave to fire, 0.95; same, but convex, 0.9; flat surface at right angles to the current of hot gases, 0.8; water-tube surface, same as last, 0.7; sloping surface at side of and inclined to the fire, 0.65; vertical surface at side of fire, 0.5; locomotive boiler tubes, — ^not more than 3 ft. from fire-box tube plate, 0.3. Horizontal surfaces underneath the fire and the lower half of internally heated tubes are not considered as effective. Ratio of Heating Surface to Grate Surface. Plain cylinder, 10 to 15: Scotch. marine and Cornish, 25 to 40; Lancashire, 26 to 33; hori- zontal return-tubular, 30 to 50; water-tube, 35 to 65; locomotive, 60 to 90. Areas of Tubes and Gas Passages. Area near bridge wall » ^ grate area. Tube area (total) =0.1 to 0.11 X grate surface for anthracite and 0.14 to 0.17 X grate area for bituminous coal, both at moderate rates of combustion (Barms). Holding Power of Tubes. Expanded* only, 5,000 to 6,000 lbs.; expanded and flared, 19,000 to 20,000 lbs. Boiler Efftciencies. For the purpose of comparison it is customary to express the evaporation in lbs. of dry steam per lb. of pure combustible, and in order to eliminate the effects of variation in the temperature of the feed- water, the results are reduced to what is termed *'the equivalent evaporation " from and at 212° F. (See page 59. ) The complete combustion 14 600 of 1 lb. of pure carbon will evaporate '_ - =15.3 lbs. of water from 900.7 and at 212°. 192 American boiler tests sunmiarized by H. H. Suplee give 10.86 lbs. per lb. of fuel, which may be considered as good practice, ordinary averages being from 6 to 8 lbs. per lb. of fuel. 12.5 lbs. evaporation is generally the best obtainable from high-grade fuels like Pocahontas and Cumberland coals. One test, however, is recorded showing an evapora- tion of 13.23 lbs. per lb. of Cumberland coal. Performance of Boilers (D. K. Clark). w=Ar^+Bc, where u^^lbs. water evaporated from and at 212° F. per sq. ft. of grate per hour, r= ratio of heating to grate surface, and c=lbs. fuel per sq. ft. of grate per hour. A and B are respectively as follows : Stationary boilers, 0.0222 and 9.56 ; marine, 0.016 and 10.25; portable, 0.008 and 8.6; locomotive, 0.009 and 9.7. materials and Tests. (From Am. Boiler Mfrs. Assn. Uniform Speci- fications.) Cast Iron. Should be soft, gray, and highly ductile; used only for hand-hole plates, man-heads, and yokes. Steel. Homogeneous open-hearth or crucible. Shell Plates not exposed to direct heat. Tensile Strength (T.S.) 65,000 to 70,000 lbs. per sq. in. ; elongation > 24% in 8 in. Phosphorus (P) and Sulphur (S)<0.035%. Shell Plates exposed to direct heat. T.S. =60.000 to 65,000 lbs., elongation > 27% in 8 in., P<0.03% and S<0.025%. HEAT AND THE STEAM ENGINE. Fire-Box Plates (exposed to direct heat). T.S. =55,000 to 62,000 lbs., elongation > 30% in 8 in., P<0.03% and S< 0.025%. Test Pieces to be 8 in. long with a cross-section > 0.5 sq. in.; width = or > thickness, edges machined. Up to 0.5 in. thickness, plate must stand bending double and being hammered down fiat upon itself. Above 0.5 in. it must stand bending 180° around a mandrel of diam. = 1.5t. Bend- ing-test pieces must not be less than 16^ in length, edges must be machined and pieces must be cut both lengthwise and crosswise from plate. Rivets must be of good charcoal iron or of soft mild steel having same Sroperties as fire-box plates. They must be tested hot and cold by driving own on an anvil with the head in a die, by nicking and bending and by bending back on themselves cold, all without developing cracks or flaws. Tubes to be of charcoal iron or mild steel made for this purpose, lap- welded or drawn. Tubes must be round, straight, free from blisters, scales, and other defects and tested under an internal hydrostatic pressure of 500 lbs. per sq. in. Standard thicknesses (B.W.G.).- — No. 13 for 1 to li in. tubes. No. 12 for 2 to 2i in., No. 11 for 2i to 3^ in., No., 10 for 3i and 4 in.. No. 9 for 4^ and 5 in. Tube Tests. A section cut from one tube selected at random from a lot of 150 or less must stand hammering down vertically when cold with- out cracking or splitting. Tubes must also stand expanding flange over on tube plate. For tubes 1 to li 2 to 2^^ 2i to 3i 3^ to 4 4i to 5 in. in diam. Length of test piece — i 1 li li Ifin. Stay Bolts of iron or mild steel must show on an 8 in. test piece as follows: Iron, T.S. >46,000 lbs., elastic limit >26,000 lbs., elongation >22% for sections under 1 sq. in. and > 20% for larger sections. For steel these values are respectively > 55,000 lbs., > 33,000 lbs., >25%, and >22%. Tests. A bar taken at random from a lot of 1,000 lbs. or less and threaded' with a sharp die to a V thread with rounded edges must bend cold 180° around a bar of same diam. without developing cracks or flaws. Another bar, screwed into a well-fitting nut of the material to be stayed and riveted over, must be pulled in a testing machine. If it fails by pulling apart its strength is measured by the T.S. If failure is due to shearing, the measure of strength is the shear stress per sq. in. of mean section in shear. (Mean section = ° o^ Xcii^umf. at half height of thread.) Braces and Stays to be of same material as stav bolts. T.S. to be determined from a 10 in. bar from each lot of 1,000 lbs. or less. All bending and hammering tests indicated above must develop no flaws, cracks, splij;ting, opening of welds, or any other form of distress. Workmanship and Dimensions. Flanging, bending, ai\d forming should be done at suitable heats, no bending or hammering, however, being allowed on. any plate which is not red by davlight at the point worked upon and at least 4 in. beyond it. Rolling to be by ^adual increments from the flat plate to a true cylindrical surface, including the lap. The thickness of bumped or spherically dished heads should equal that of a cylindrical shell of solid plate whose diam. is equal to the radius of curva< ture of the dished head, an increase of t being taken to allow for rivet holes, manholes, etc. Rivet holes should be perfectly true and fair, either drilled or cleanly punched, burrs and sharp edges to be removed by slight countersinking and burr-reaming both before and after sheets are joined. Under sides of original rivet heads to be flat, square, and smooth. Allow length of li diam. for stock for heads, for f to H in. rivets, and less for larger siaes. Allow 5% more stock for driven head for button-set or snap rivets. For machine-riveting, total pressure on die = 35 tons for f in. rivets, 57 tons for II in. rivets, 65 tons for 1 in., and 80 tons for 1^ and H in. rivets. Ap- proximately, make d of rivet hole=2< (of thinnest plate), p"=3d, distance between pitch lines of staggered rows»=0.5p'', lap for single-riveting = p" lap for double-riveting=1.333p" (add 0.5p" for each additional row of rivets). For exact dimensions make resistance to shear of aggregate rivet sections > 1.1 X T.S. of net metal. Holes <| in. in steel may oe punched, abov^ I, punch and ream, or drill. Drift-pins to be used onhr to pull plates into position, — never to enlarge holes. Calking to be done only STEAM-BOILERS. 89 with round'Hose tools, calking edges to be planed, sheared, or chipped to a bevel. Finishing may be done with a square-nose tool if care is taken to avoid nicking the lower plate. Safe working pressure per sq. in. on flat surfaces; p = Ct^-ir(p")2^ where < = thickness of plate in 16ths of an inch, p" = pitch of stays in in., and C = 112 for plates A in. find less, with riveted screw stays, 120 for plates >iV iJQ. with riveted screw sta^s, and 140 for all plates where the screw stays have in addition a nut inside and outside the plate. This latter is imperative when the feed-water contains salt, acids, or alkali. Tube holes should be punched i in. less than tube diam. and reamed or drilled, holes being slightly countersimk on both sides* Finished holes to be from A to tV in. larger than tube, according to size. . If copper ferules are used, the ferules should bv a neat fit in the holes. The tube sheet should be annealed after punching and before drilling, and the tube ends before setting. Tubes to project A in. beyond sheet for each inch of diam. Tubes to be expanded only imtil tight. Ends which are exposed to direct flame must be flanged, beaded over and slightly re-expanded- Copper ferules (No. 18 to No. 14 wire gauge) to be used in fire-tube boilers on ends exposed to direct heat. Stay bolts to be carefully threaded and holes tapped with a tap extending through both plates. Bolts to project t diam. for riveting over. Tnickness of nuts for screw stays > 0.6 diam. of stay. Pitch of stays < JO in. If welding is necessary in braces and stays take strength of welded bar=<0.8XBtrength of solid bar. Brace rivets subject to oblique pull are allowed to bear only one-half the stress of seam rivets. Manholes to be flanged inwards on a radius >3t and are to be reinforced by W.I. or steel rings, which are shrunk on. Domes when unavoidable to be flanged down to shell, and the shell to be flanged up inside the dome or else reinforced by a collar flanged at the joint, flan^ being double-riveted. Drums to be put on with steel collar flanges >| m. thick, double-riveted to shell and drum and single-riveted to iieek or leg, or, the flanges may be formed on the legs. Safety factors rivet seams, 4.6; flat surfaces, bumped heads, stay- bolts, braces and stays, 6. Hydrostatic test pressure should not exceed the working steam pressure by more than i of itself, and this excess should not be greater than 100 lbs. per sq. in. The temperature of testing water should not be less than 125° F. Board of Trade (B. T.) and U. S. Statute Proportions and Bules. Materials. Shells ; (B.T.) T.S. from 27 to 32 tons, elongation in 10 in. > 18% (if annealed, >20%); 2 in. strips to stand bending imtil sides are parallel and not >3t apart. (U.S.) When < = or<0.5 in., contraction must be — or>60%, from 0.6 to 0.76 in.,>46% and above 0.76 in.,>40%. Stays (B.T.). Same T.S. as shells, elongation in 10 in.>20%. Steel stays welded or worked in fire not to be used. Allowable lo£td «= 9,000 lbs. per sq. in. on net section. (U.S.) Reduction of area must ' be > 40% if test bar is > 0.76 in. in diam. Allowable load = 6,000 lbs. per sq. in. Notation for the following Boiler Proportions Z> = boiler diam., f*" thickness, «i = thickness in Idths, p=greatest pitch between stays, L — pitch of flanges, (f = outside diam. of tubes, TF = width of flame box, ii« length of girders, pi = pitch of bolts, Z)2= distance between centers of girders, <2i= depth of girders, t2—8\un of girder thicknesses, Z>8=" least horisontal distance between centers of tubes, ^2= inside tube diam , Wi — width of combustion box from tube-plate to back of fire-box; all in inches. P and T are working pressure and tensile strength in lbs. per sq. in., 5=surface supported in sq. in., Z>i*=outside flue diam. in ft., I — length of furnace (up to 10 ft.) in feet, F=»8afety factor, = 4.6, fi = per- centage of strength of joint compared to solid plate. Boiler Shells (B.T.). P = 2BTt-i-DF. (U.S.)P = r<+3D for single- riveting. Add 20% for double-riveting. Flat Plates (B.T.). P = C«, + l)2-f-(-S-6). C==»126 for plates not exposed to heat or flame, stays fitted with nuts and washers, the latter at least 3 Xdiam. of stay and having a thick- ness =f< of plate. = 187.6, same, but with diam. of washers = I pitch of stajrs, and of thickness not less than that of the plate. «=»200, same, but with doubling plates in place of washers, whose width = fX pitch of stays, and thick ne8s= that .of plate. -B 112.6, same, but stays fitted with nuts only. 90 HEAT AND THE STEAM ENGINE. C—7b for plates exposed to heat or flame, steam being in contact with the plates, stays fitted as where C = 125, above. = 67.5, same condition, but stays fitted with nuts only. «100 for plates exposed to heat or flame, water being in contact with the plates, stays screwed into plates and fitted with nuts. — 66, same condition, but stay« with riveted heads. (Above values for steel plates; for iron plates take 80% of same.) (U.S.) P = C<,-Hp2. C»112 for plates iV in. and under, with screw stay bolts and nuts, with plain bolt ntted with single nut and socket, or with riveted head and socket. » 120 for plates thicker than -h in. for same fastenings. »140 for flat surfaces, stajrs fitted with inside and outside nuts. = 200, same as for C = 140, but with the addition of washer riveted to plate, whose thickness is at least QM of plate and whose diam. = 0.4 X pitch of stays. N.B. Plates fitted with double angle-irons and riveted to plate with leaf at least ^t of plate and depth at least iX pitch are to be allowed the same pressure as that determined for plate with washer riveted on. No brace or stay bolt in a marine boiler to have a pitch greater than 10.5 in. on fire-boxes and back connections. Plates for FtangliiK (B.T.). -P=^^'(5-^^^^). This formula is for the strength of furnaces stiffened with flanged seams where L < 120t— 12, the flanges being properly designed and formed at one heat. Furnace Flues. Long furnaces (B.T.). P-"C<2h-(Z+1)Z)i. where l>(11.5t — 1). C = 88,000 for single-strap butt-joints single-riveted, —99,000 for welded joints or butts with single straps double-riveted, and also for double-strap butt joints single-riveted. P from above formula should not exceed the value given by the following formula for short and patent furnaces. Short Furnaces, Plain and Patent (B.T.). P'^ct+Di, where c- 8,800 for plain furnaces: =14,000 for Fox (max. and min. <«=f and A in. and plain part < 6 in. long); =13,500 for Morison, same conditions as Fox ; =14,000 for Purves-Brown (max. and min. <•=! and A in., plain part < 9 in. long). Long Furnaces (U.S.). P = 89,600<2-*-fZ)i {I not to exceed 8 ft.). Short Furnaces (U.S.). P=c<-5-Di, where c= 14,000 for Fox (Di = mean diam.); =14,000 for Purves-Brown (Di=flue diam.); =5,677 for plain flues > 16 in. diam. and <40 in. diam. when not over 3-foot lengths. Stay Girders (B.T.). P = Cd^%-i-{W -Pi)D^u where C = 6,600 for 1 bolt, =9.900 for 2 or 3 bolts and =11,220 for 4 bolts. Tube Plates (B.T.). P = 20,000«(D3-d2)-*- W^i^s- Crushing stress on tube plates caused by pressure on top of flame-box to be < 10,000 lbs. per sq. in. Air Passages through grate bars should be from 30 to 50% of grate area, the larger the better, in order to avoid stoppage of air supply by clinker, but with clinkerless coal much smaller areas may be used. COMBUSTION. Combustion or burning is rapid chemical combination accompanied by heat and sometimes light, during which heat is evolved equal to that required to separate the elements. In the bumine of a simple hydrocarbon (e.g., marsh gas), the combus- tion being complete. Marsh Gas -f Oxygen = Carbon Dioxide + Water (Steam) ; CH4 + 2O2 = CO2 + 2H2O or, taking the atomic weights of C, H, and O as 12, 1, and 16, respectively, (12-»-4) + 2(16X2) = [12-l-(16X2)] + 2(2-l-16), i.e., 161b. -I- 641b. = 441b. -I- 36 lb. or lib. + 41b. yields 2.751b. -f- 2.251b. Also, 1 lb. C burnt to CO2 yields 14,600 B.T.U. and 1 lb. H burnt to HjO yields 62,000 B.T.U., and, as 1 lb. CH4 = i lb. C-hi lb. H, then 0.751b. C + O yields 14,600X0.75 = 10,950 B.T.U. 0.25" H + '* 62.000X0.25 = 15,500 '* Total = 26,450 *• COMBUSTION. 91 Experimentally, about 2,800 B.T.U. less are obtained, the loss being required to effect the work of decomposins the C and H. Good, dry bituminous coal contains on the average, by weight Carbon, 83.5%; Hydrogen, 4.6% ; Oxygen, 3.15%; Nitrogen and Sulphur (inactive elements), 8.75%. In 100 lbs. of fuel the 3.15 lb. O is akeady united to (iX3.15) 0.4 lb. H in the form of water, consequently this H does not assist in combustion. This leaves 83.5 lb. C and 4.2 lb. H to be dealt with. Now, 12 lb. C unite with 32 lb. O to form CO2 (1 : 2.66) and 2 lb. H unite with 16 lb. O (1:8) to form HjO. Consequently 83.5 lb. C require 83.6 X 2.66 = 222 lb. O 4.2 " H ^' 4.2X8 = 33.6*' ** Or, for 100 lb. coal, total = 255.6 " *' Air-23% + 77% N; therefore 21 100:: 255.6 + 100.11.1, or 11.1 lb. of air are tneoretically needed for the combustion of 1 lb. of the coal. (In Eractice the theoretical amount must be multiplied by 1.5 for gas furnaces, y 1.5 to 2 for good grates, and by 3 or more for defective furnaces.) Also, 0.8351b. CX 14,600 = 12,191 B.T.U. 0.042 " HX 62,000= 2,604 " Total B.T.U. per 1 lb. coal = 14,795 The Calorific Taiue of a Given Fuel may be expressed by the follow- ing modification of Dulong's formula: B.T.U. per lb. = 14,600 C+ 62,000 (h-^) +4,000 S, where the pro- portions of C, H, O, and S are determined by analysis. Where a complete analysis of the coal is not obtainable the following formula of Otto Gmelin may be used B.T.U. per lb. = 144(100 — (w+a)] - 10.8 tDC, where w and a are the percentages of water and ash, and c is a constant varying with the amount of water. When w<3%, c=4; when w is between 3 and 4.5%, c = 6; w bet. 4.5 and 8.5%, c=12; w bet. 8.5 and 12%, c-10; w bet. 12 and 20%, c=8; w bet. 20 and 28%, c = 6; u;>28%, c = 4. Also, when C and Ci are the percentages of fixed and volatile carbon, respectively, and H the percentage of hydrogen, B.T.U. per lb. = ( 14,600 C + 20,390 C, + 62,000 H ) -h 100. American Coals. Approximate Analyses and Caloriflc Valttes. Mois- ture. Volatile Matter. Fixed Carbon. Ash. Sul- phur. B.T.U. per Lb. Coal. Anthracites: *E. middle field, Pa. *N. ;. W. *• . •* **. Semi-anthracite : Loyalsock, Pa Semi-bituminous . ♦Clearfield, Pa * Cumberland, Md . . * PocahontaStVa. . . ♦New River, W.Va. Bituminous : * Youghiogheny, Pa. Connellsville, Pa. .. . Brazil, Ind * Big Muddy, lU Streator, 111 Rosyln,Wash (Cle-Elum.) Cokes : Connellsville, Pa. . . . Chattanooga, Tenn.. Birmingham, Ala. . Pocahontas, Va. . . . 4.12 3.42 3.16 1.3 .81 .95 .85 .76 1.03 1.26 8.98 7.7 8.3 6.34 (B.T.U %CX 3.08 4.38 3.72 8.10 21.10 19.13 18.60 18.65 36.49 30.10 34.49 31.9 37.63 37.86 pr. lb. = 14,600) 86.38 83.27 81.14 83.34 74.08 72.70 75.75 79.26 59.05 59.61 50.30 53 45.93 48.30 88.96 80.51 87.29 92.53 5.92 8.20 11.08 6.23 3.36 6.40 4.80 1.11 2.61 8.23 6.28 7.4 8.14 7.59 9.74 16.34 10.54 5.74 0.49 .73 .90 1.03 .42 .78 .62 .23 1.81 .78 1.39 .49 .81 1.595 1.195 .597 13,578 13,434 12,958 14,247 14,985 14,461 14,854 15,429 14,262 13,946 12,356 12,895 12,047 12,429 12,988 11,754 12,744 13,509 92 HEAT AND THE STEAM ENGINE. Coals marked * are generally selected for boiler tests on accoimt of avail- ability, excellence of quality, and adaptability to various kinds ui furnaces, grates, boilers, and methods of firing. The number of B.T.U. per lb. of coal is calculated by means of Goutal's formula: B.T.U. per lb. of coal = 14,760C+aF, where C = percentage of fixed carbon in the coal, F = percentage of volatile matter in the coal, and a=°a variable depending on the ratio Vi of the volatile matter to the amount of combustible m the coaL Values of ar Vi=F+(F + C)= 0.05 0.1 0.15 0.20 0.25 a -26,100 23,400 21,060 19,620 18,540 Vi = 0.30 0.35 0365 0.385 0.40 a -17,640 16,920 16,480 15,000 14,400 This formula is fairly accurate where the percentage of fixed carbon is above 60; whenever exact results are required a calorimetric determina- tion of the heating value of the p£u*ticular fuel should be made. Wood. 1 cord = 128 cu. ft., about 75 ft. of which are sohd wood, 2.25 lbs. of dry wood are about equal to 1 lb. of soft coal in heating effect. Average wood (perfectly dry) has a calorific value of about 8,200 B.T.U. per lb. ; if ordinary, air-dried (25% moisture), about 5,800 B.T.U. per lb. Petroleum. Average composition =0.847 C + 0.131 H +0.022 O, Sp. gr. = 0.87. B.T.U. per lb. -20,318 (Beaumont, Tex., crude oil, 18,500 B.T.U.). Distillates from Petroleum (CioH^ to C!32H64) vary from 71.42 to .77% C, and from 28.58 to 26.23% H. Sp. gr. =0.628 to 0.792. Boiling-point varies from 86® to 495° F. B.T.U. per lb., from 27,000 to 28,000. Gas Fuels (B.T.U. per 1,000 cu. ft.): Natural gas, 1,100,000; coal-gas, 640,000 to 675,000; water-gas, 290,000 to 327,000; gasohne-gas, 517,000; producer-gas, — anthracite, 137,000; bituminous, 156,000. Miscellaneous Fuels (B.T.U. per lb.): Spent tanbark, 4,280 (30% water) to 6,100 (dry); straw, 5,400 to 6,500; bagasse (sugar-cane refuse), 3,750, when fibre = 45%; com, 7,800 (ordinary condition) to 8,500 (dry). Draft. Chimneys. Kent. Gale-Meier. Ing. Taschenbuch* Area, A "^^ 0.07F* Diam., d- 0.242/*°** Height. * = (4^' if (I)' 0.216(f )%«. Where F = total coal burnt per hour in lbs., < = temp. of discharge gases in F.°, (? — sq. ft. of grate area, <2= internal diam. in feet (A in sq. ft., h in ft.). The larger results obtained from the Taschenbuch formulas are probably due to the inferior evaporative power of German coals. /7 64 7 95\ Intensity of Draft (/). / in inches of water = A(-^^ ^), where ^2 ■'i 7^2 and Ti are respectively the absolute temperatures of the external air and the chimney gases. / at the base of ordinary chimneys ranges from 0.5 to 0.75 in. In locomotives the vacuum induced by the steam-blast varies from 3 to 8 inches of water in the smoke-box and is about i as much in the fire-box. The best value of Ti-27'2, or about 585° F. Temperature of Chimney Gases. To determine same approximately, suspend strips of the following metals in the chimney and note those which melt. Metal Sn Bi Pb Zn Sb Melting-point, F.°. . 456 518 630 793 810 Telocity of Chimney Gases. . . 8'V^chimneyterap. — air temp.) V m ft. per sec. = ^ ^ ^ . . r 3.3 X chimney temp. (Temp, in F.*^. Draft Pressures required for Combustion of Fuels (in inches of water). Wood, 0.2 to 0.25; sawdust, 0.35 to 0.5; do., with small coal. BOILER ACCESSORY APPARATUS. 93 0.6 to 0.75; steam coal, 0.4 to 0.75; slack, 0.6 to 0.9; do., very small, 0.75 to 1.25; semi-anthracite, 0.9 to 1.25; anthracite, 1.25 to 1.5; do., slack, 1.3 to 1.8. Sate of Ccmbustion (lbs. of fuel per hour per sq. ft. of grate area). Anthracite. 5 to 15; bituminous, 4 to 26. Ordinary combustion may be increased 50% by means of artificial draft. In locomotives the rate of combustion ranges from 45 to 85 and even 120 lbs. Low-grade or refuse fuels may be utilized with artificial draft, the high rate of com- bustion compensating for the low evaporative power of the fuel. Blechanical Stoking. In the Jones underfeed stoker coal is fed into a hopper and pushed forward from the bottom thereof by a steam- actuated plunger into the retort or fire-box from beneath, air being intro- duced at the top of retort. As the fresh coal approaches the fire from beneath its gases are hberated by the heat and pass upwards through the fire and are consumed, — aiding in the production of heat, — and the coal reaches the fire practically coked, the production of smoke being thus avoided. The manufacturers (Underfeed Stoker Co., Ltd., Toronto) claim that its use will effect a saving of from 18 to 25% of the fuel as com- pared with hand-firing. BOII.EB ACCESSOBT APPABATUS. Feed- Water Heating obviates in large measure the strains that would otherwise be induced by introducing water into the boiler at ordinary temperatures, and also affords considerable economy. Saving in per cent by heating feed-water with exhaust steam » ^ — j-J, wl^re ^= total heat of 1 lb. steam at boiler pressure, Ai = total /i — »i heat of 1 lb. water before entering heater, and A2=same after leaving heater. For average conditions there is an approximate saving of 1% for each increase of ll*' in the temp, of feed-water, which may be heated as high as 210** F. Green's Economizer is a feed-water heater composed of tubes so situated in the flues between boiler and chimney as to intercept some of the heat of the waste gases. As the temperature of steam from 100 to 200 lbs. pressure ranges from 338° to 388° F., all heat in chimney gases above these temperatures is wasted unless a portion of it can be absorbed in some such manner. Average chimney temps, reach 600° F. Economizers effect a gain in evaporative power of from 6 to 30%, fair results being set at 10 to 12%, with a cooling of flue gases of from 150° to 250° F. Condensers. In condensing the exhaust steam from an engine a partial vacuimi is formed and the gain in power may be based on the mcrease of the mean effective pressure by about 12 lbs. per sq. in. Jet Condensers, in which the exhaust is met by a spray of cooling water, should have a capacity of from ^ to i that of the low-pressure cyUnder. Quantity of water required = 25 to 30Xwt. of steam to be condensed. Temp, of hot-well = 110° to 120° F. Surface Condensers should have vertical brass tubes for maximum efficiency and the water should flow downwards through them. Tubes should be as long as practicable and of small diam. (0.5 to 1 in.). (Pooling surface of tubes = 1 to 3 sq. ft. per I.H.P., according to climate. 12.5 lbs. steam condensed per sq. ft. per hour is good practice. Q of circulating water = 30 Xwt. of steam condensed. IT . TJ ___ . Q for jet condenser in lbs.= ^ - , Q f or surface condenser = ; — —, where t — ti t2 — *1 ff = 1,114° F. = total heat of 1 lb. exhaust steam, < = temp. of hot-well in F.°, <i=entering temp, of cooling water, and <2 = temp. of water when leaving the condenser. Area of injection orifice = lbs. water per min. + 650 to 750, or, =area of piston -h 250. Evaporative Condensers. In these the exhaust is led through a large number of pipes cooled externally by trickhng streams of water. This water evaporates, thus condensing the exhaust steam in the pipes, which is then pumped back into the boiler. Used where economy in water consumpticm is imperative. In well-designed condensers of this 94 HEAT AND THE STEAM ENGINE. class 1 lb. of water will condense 1 lb. of steam, as against the 20 to 30 lbs. of water required in jet and surface condensers. Alr-Pumjps in all conden-sers abstract the water of condensation and the air it originally contained when entering the boiler. In jet condensers they also pump out the condensing water and its content of air. TTie size of an air-pimip is calculated from these conditions, allowances being r I H P mode for efficiency. Volume of Air-Pump in cu. ft. = — (q +Q) = — — '—^ X ci , n r.p.m. where n=«number of useful strokes per min., g=cu. ft. of water condensed per min., Q = cu. ft. of cooling water per min., c="2.8 for single-acting and 3.5 for double-acting pumps. (For jet condcn.sera onlj'.) ci=0.41 for single-acting pump and jet condenser, =0.17 for si ngi .^-acting pump and surface condenser, and =0.27 for double-acting hcrizontal pump and jet condenser. Vol. of sin^e-acting air-pump = Vol. of low-pres. cyl.-i-23. Circ ulating Pumps. Capacity = Q-H n. Diam. of cylinder in inches = 13.55'^Q -5- (nX length of stroke in feet). (For Q and n see Air- Pumps.) The area through valve-seats and past the valves should be large enoiigh to permit the full quantity of condensing water to flow at a velocity <400 ft. per min. Fusible Plugs are screwed into those portions of boilers where the heating surface first becomes exposed from lack of water. They have a core of fusible metal at least 0.5 in. diam. tapered to withstand internal pressure. The U. S. Gov't specifies Banca tin which melts at 445° F. (2 Tin + 1 Bismuth melts at 334° F., 3 Tin -I- 1 Bismuth at 392° F.). Safety-Valves, Area (U.S.). Lever valves: area»0.5 sq. in. per sq. ft. of grate area. Spring-loaded valves; i sq. in. per sq. ft. of grate area. Spnng-loaded valves for water-tube, coil, and sectional boilers carrying over 175 lbs. pressure must have an area>^ sq. in. per sq. ft. grate area. Seats to be inclined 45° to axis. Spring-loaded valves to be supplied with a lever which shall raise valve from seat to a height equal to at least \ diam. of opening. (B.T.) Area in sq. in. = (37.5 X grate area in sq. ft.)-s-(gauge pres- sure +15). Philadelphia Rule; Area in sq. in. = (22.5 X grate area in sq. ft.) -*- (gauge pressure + 8.62). Ingenieurs Taschenbuch a =0.0644r — ' where a=«area of valve in sq. in. per sq. ft. of heating surface, p"=max gauge pressure, F = cu. ft. of steam per lb. at pressure p. __ Injectors (Live-Steam). Water injected in gals, per hour «=1,280D*>/P, where D = diam. of throat in ins., and P = steam pressure in lbs. per sq. in. , , , . . cu.ft. of feed-water per hour(gross). Area of narrowest part of nozzle in sq.m. =■ ■ . 800 V Pressure in atmospheres One lb. steam will inject about 14 lbs. water. An exhaust-steam injector will feed against pressures < 80 lbs., the feed being at about 65° F. An auxiliary live-steam jet can be attached to feed against 110 lbs. pressure, and, by compounding another live-steam injector with it, a boiler may be fed up to about 200 lbs. pressure, the feed reaching boiler in this case at about 250° F. o • r r i * • ^ u Injector vs. Pump. Savmg of fuel over amount required when a direct-acting pump feeds at 60° F. (without heater, boiler evaporating 10 lbs. water at 212° F. per lb. of fuel). Injector feeding at 150°, no heater, saving. 1.5% •• •• through heater (from 150° to 200°), " 6.2^^ Direct-acting pump through heater (from 60° to 200°), " 12.1% Geared " " " ( " 60 " 200°), " 13.2% Steam-Pipes (B.T.). <f=inside diam., <-=thickness, both in inches; p = pressure in lb. per sq. i"- Copper Pipes, brazed, < = 6;oOO"'"^ *°*' so^**-**^*^^' '"eioOO"*"^ *°' Lap- welded Iron P»Pes, / = g^; Cast-iron Pipes, < = g^+^ in. Provision should be made for expansion in long lines, which amounts to about 1 in. in 50 ft. for the range of temperatures usually employed. INCRUSTATION AND CORROSION. 95 INCRUSTATION AND CORROSION. Incmstation or scale is the hard deposit in boilers resulting from the precipitation of impurities from water boiling at high temperatures. Scale of 1^ in. thickness will reduce boiler efficiency i, and the reduction of efficiency increases as the square of the thickness of scale. A larger amount than 100 parts in 100,000 of total solid residue will generalljr cause trouble- some scale, and waters containing over 5 parts in 100,000 of nitric, sulphuric, or muriatic acids are liable to cause serious corrosion. Prevention and Cure of Boiler Troubles due to Water. Trouble. Troublesome Substance. Remedy or Palliative. Incrustation. . Sediment, mud, clay, etc. Filtration, blowing-off. Readily soluble salts. Blowing-off. Bicarbonates of magnesia, Heating feed and precipitat- lime, and iron. ing by addition of caustic soda, lime, magnesia, etc. Sulphate of lime. Addition of carbonate of soda or barium chloride. Priming Carb. of soda in large Addition of barimn chloride. amounts. Organic matter (sewage). Precipitate with alum or ferric chloride and then filter. Corrosion Oi^anic matter. Ditto. Acid in mine waters. Add alkali. Dissolved carbonic acid and Heating feed, addition of oxygen. caustic soda, slacked lime, etc. Grease. Slacked lime and filtering. Carb. of soda. (Substitute mineral oils.) Many scale-making minerals may be removed by using a feed-water heater and emplo3ang temperatures at which the minerals are insoluble and consequently precipitate, when they may be blown off before passing to boiler. Phosphate of lime, oxide of iron and silica are insoluble at 212* carbonate of lime, at 302*. and sulphate of lime at 392° F Kerosene has been successfullv used in softening and preventing scale and should be introduced into the feed-water in quantities not exceeding 0.01 qt. per H.P. per day of 10 hours. Tannate of Soda Compound. — Dissolve 50 lb. sal soda and 35 lb. japonica in 60 gal. water, boil and allow to settle. Use ^V qt. per H.P. per 10 hours, introducing same gradually with the feed-water. Grooving is the cracking of plate surface due to abrupt bending under alternate heating and cooUng. It is generally found near rigid stays and its ill effects are augmented by corrosion. It may be avoided by providing for sufficient elasticity along with strength and by rounding the stay edges at the plate. INTERNAL-COMBUSTION ENGINES. Internal-combustion engines are divided into two classes. In the first an explosive charge of gas and air (or a vapor of alcohol, gasoline, or kerosene, mixed with air) is drawn into the cylinder, compressed, ignited, expanded, and then exhausted. The ignition produces a practicidly instantaneous explosion. , In the second class (e.g., Diesel motors) a charge of air is drawn in and IS riused by compression to a temperature high enough to i^ite the oil, gasoline or other fuel which is sprayed into the cylinder dunng a certain portion of the power stroke. The combustion in this case is gradual and extends over the period of the stroke during which the fuel is injected In simple engines there are four strokes in the cycle of operation 1st stroke, drawing in of explosive charge; 2d (return) stroke, compres- sion of the charge; 3d stroke, ignition and expansion (power stroke); 4th (return) stroke, exhaust of the burnt gases. The Ist, 2d, and 4tn strokes consume from 5 to 10% of the power developed on the 3d stroke. (For indicator card, see Fig. 12, T.) 96 9 HEAT AND THE STEAM ENGINE. In two-cyole engines the charge is compressed in a separate cylinder, ignition and expansion taking place on the 1st or outward stroke, of engine and* exhaust on the return stroke, — there being one impulse for each revolution of fly-wheel. Large engines are also constructed so as to give an impulse on each stroke. Fuels. The thermal efficiency of an internal-combustion engine is increased by high compression, the only limit being that the temperature at the end of the compression must not approach near to that of ignition. The temperature of ignition varies inversely as the number of B.T.U. contained in the charge, and rich gases, therefore, should not be highly compressed save in well diluted charges. The limits of compression may be extended by cooling the gases undergoing compression, as in the Banki motor, where water is sprayed into the cylinder to absorb the heat given out during compression, and also as in the Diesel engine, where the air is compressed to its final pressure before the fuel is injected. Rich Gases (containing over 350 B.T.U. per su. ft.). Coal, coke-oven, and natural gases. Rich Mixtiu'e. Lean Mixture. Ratio of gas to air 1:6 to 1:7 1:10 to 1:15 Temperature of ignition. . . . 1.000 to 1,100® F. abs. 1,200 to 1,380° F. abs. Compression, lbs. per sq. in.. 65 ' /u 75 " 115 M.E.P. *♦ ** " ** 70** 85 65" 78 Explosion pressure per sq. in. 210" 285 285" 355 Lean Gases (containing less than 350 B.T.U. per cu. ft.). Dowson, producer, and blast-furnace gases. Ratio of gas to air 1 : 1 to 1 : 2 Temperature of ignition 1,300 " 1,475° F. abs. Compression Il5 '* 215 lbs. per sq. in. Mean effective pressure 65 " 78 " " " " Explosion pressure 255 * * 355 " " " " The gas and air should be thoroughly mixed before ignition, which, for rich mixtures, is either by a hot tube, a valve -governed flame, or by an electric spark. For lean mixtures the electric spark is used. Liquid Fuels. Gasoline, Kerosene, Naphtha, Benzine. Alcohol. Ignition temperature, ° F. abs 930 to 1,020 985 to 1 ,075 Compression, lbs. per sq. in 40 " 70 55 * * 115 (Banki motor) 170 " 210 (Diesel) 450 " 500 Explosion pressure, lbs. per sq. in. . . . 170 " 285 140 " 285 (Banki) 565 , M.E.P.. lbs. per sq. in 57 ^* 78 60 '* 70 Liquid fuels are vaporized before mixing. Light oils (gasoline, etc.) are vaporized by the heat of the air drawn through or over them, or they may be atomized. Heavier oils require heating in order to vaporise. Gasoline-gas is usually ignited by an electric spark, — heavier oils by the hot tube. Average Values for Compression (Lucke). Kerosene and city gas, 80 lbs.; gasoline, 85 lbs.; natural gas, 115 lbs.; producer gas, 135 lbs.; blast-furnace gas, 155 lbs. (All pressures are absolute.) Fuel Consumption (Ch) per B.H.P. Hour, and actual thermal efficiencies C^). 6 H.P. 25 HP. 100 H.P. Ck nw €h Vw Ch lite Coal gas, cu. ft... 19 0.20 15.5 0.24 13.8 0.27 Producer gas, " **.. 105 to 0.17 85 to 0.21 75 to 0.24 115 92 80 Blast-furnace gas, " ".. 115 0.20 100 0.24 Coke-oven gas, " ".. 30 0.19 24.7 0.23 Gasoline, lbs. .. 0.66 0.19 0.55 0.23 Kerosene, " ..1.2 0.11 1.02 0.13 Alcohol. 90% ** ..1.1 0.22 0.92 0.26 Petroleum, crude, ** ..0.55 0.25 0.61 0.27 0.44 0.315 (OieBel motors) INTEBNAlnCOMBUSTION ENGINES. 97 Properties of Fuels. Coal-gas, average. . . ♦• N.Y.aty. Producer-jjas. Anthracite Ck)ke Water-gas (coke). . . Blast-fumaoe gas. . . Coke-oven gas Natural gas do. Pittsbui^h . . . * Acetylene Petroleum (Kerosene) .... Benzine, gasoline. Alcohol, grain (90%) • ' wood. . . . B.T.U. Lbs. per Cu. Ft. per CJu. Ft. (H.) (Atmos. 650 .035 710 to 720 140 .062 to 130 .075 275 .044 106 .08 450 .042 1,000 to 1,100 .0458 495 to 585 1,550 B.T.U. per Lb. 18,500 50 22,000 18.000-20,000 43.8 10,900 51.9 8,300 Cu. Ft. per Lb. Pressure.) 28.5 16 to 13.5 22.7 12.4 24 21.83 .02 .0229 J .019 Cu. Ft. Air Re- quired for Com- bustion of 1 Cu. Ft. Gas. Theoret. Actual. 5.6 to 6.5 .85 to 1 2.4 .75 5.3 9 12.5 9 to 10 1.1 to 1.4 3 to 4 1 to 1.2 7 12.5 18 to 20 Cu. Ft. Air per Lb. Fuel. 250 to 350 185 96 240 to 320 125 to 190 * One pound of calcium carbide liberates 5.75 cu. ft. of acetylene gas. CoolinflT Water (when entering cylinder jacket at about 60° F. and leaving at about 150° F.) should be supplied at the rate of 40 to 45 lbs. per hour per I. PI. P. (or 5 to 5.5 gal.). Supply tanks should have a capac- ity of 20 to 30 gal. per I.H.P. Eifflclencles. Actual thermal efficiency, >^ = 2,545 ■*-HCA. efficiency. ijin = B.H.R,-5-I.H.P. Indicated thermal efficiency. Theoretical thermal efficiency, '?t = (1.25 to 2)i)i. (Lucke). Mechanical Average Values of vm ( I.H.P. of Engine. 500 and larger. Four-cycle. .81 to .86 25 to 500 79 •* .81 4 •• 25 74 •* .80 Two-cycle. .63 to .70 .64 *• .66 .63 •• .70 Brake Horse-Power = asTmiimE -f- ( 1 2 X 33,000 ) = (nd^sE X 65 X 0.85) + (4Xl2X33,000)=O.OOOl096d2«J^, where a = area of cylinder in 8q.in.» 0.7854d2, » = stroke in inches, pm = mean effective pressure (average » 65 lbs. per sq. in.), lym — .85, j& — number of explosions per min. = r.p.m.-!-2, for a four-cycle engine. Piston Speeds. Average practice in ft. per min. = 6004-0.2XH.P. . Talve Setting* The exhaust should close when engine is on center; the inlet should open about 5° after center is passed and continue about 10** beyond center after compression has begun. Ratio of Clearance to Stroke (— ). where c= volume of clearance space in cu. in.-*- area of cyl. in sq. in. Natural gas 0.3 Rich gas, rich mixture 0.47 •* .lean ** 0.26 T^an ga.s 0.18 Benzine . 54 (Banki) 0.146 Petroleum, Alcohol 0.42 (Diesel) 0.072 +». Compression. 100 lb. per sq. in to 0.77 65to 40 •• 0.38 115 •• 80 *• " 0.26 170 *• 115 '• •• 1.44 56 " 28 • •* *• 0.177 210 •• 170 " " *♦ •• '• 0.77 70 •• 42 '• *• •• •• •' 0.077 600 " 450 •* • 98 HEAT AND THE STEAM ENGINE. , = 100(1 + ^) Expansion and Compression Laws. PF"=PiFi«. For expansion n ranges from 1.25 to 1.4, and for compression, from 1.2 to 1.5. For expan- sion, n is generallj^ taken at 1.35. and at 1.3 for compression. If n is taken at 1.33, the following formulas may be used: Pressures and Temperatures (Absolute). Let P = suction pressure in lbs. per sq. in., Pc = compression pressure, Pe=explosion pressure, Pr = exhaust pressure, 7" = initial temperature of charge in degs. F. absolute, 7'e = temp. at end of compression, rc= explosion temperature, 7'r= exhaust temperature, 8= stroke in in., and c = clearance expressed as inches of stroke. Then,Pc = P'5^t(s-f'c)-5-c]4. r for scavenging engines = + 461; for n on -sc avengin g engines , T = 120[l +(c-h«)] + 461. Tc='T^Pc-i-P^T^l(8 + c)-^cl Te = Tc + R if scavenging; if not, Te = rc + /2-*-[14-(c-5-«)], where R is the rise of temperature due to explosion and is obtaine d from a table which follows. Pe'^PeTe-i-Te. Pr'= Pe-^y (^ j , where «i= inches of stroke completed at point of release. rr=re-h>^j/Pe-5-Pr = !re-5-^[(»i + c)-^-c]. Ratio of Air to Gas (volumetric), a = (C-^ 50) : 1 for best economy a = (C-J-60) : 1 for maximum possible load. C = calorific value of gas m B.T.U. per cu. ft. Calorific Value of Explosive Mixture, Ci = C-J-(a + l). Properties of the Constituent Elements of Gases. (32° F., atmospheric pressure.) Hydrogen, H Marsh-gas, CH4 Ethylene, C2H4 Carbon-monoxide, CO. Carbon -dioxide, C02. . Nitrogen, N Oxygen, O Air Gas - engine exhaust (coal gas) Specific Heat. K- 2.414 .470 .332 .176 .154 .173 .156 .169 .189 3.405 593 404 248 217 244 218 .2377 .258 Lbs. per cu. ft. 00559 0445 0778 0777 .1221 0778 0888 .08011 Lbs. Oxy- gen per lb. Gas for Com- bus- tion. 8 4 3.434 .571 Cu. ft. Air re- quired byl cu. ft. of Gas for Com- bus- tion. 2.43 9.66 14.5 2.41 H CH4 CO B.T.U. per lb. of Constituent Gas. High. Low. 61,560 23,832 21,384 4,392 51.840 21,438 20.016 4,392 B.T.U. per cu. ft. High. Low. 344.12 1060.52 1663.68 341 . 26 289.79 954 1567.24 341 . 26 (Weights in above table have been calculated from the latest values given to atomic weights. The B.T.U. values have been taken from Des Ingenieurs Taschenbuch. The values for specific heat are taken from a table by W. W. Pullen, in Fowler's Pocket-Book. ) Calculation of the Calorific Value of a Gas (1 cu. ft. at 32° F.). The table on page 99 gives the calculations for a high-grade coal-gas. The difference between the high and low values of the B.T.U. in the tables is due to the heat of condensation of that amoimt of steam which results from burning the hydrogen in one cubic foot of gas. The low value should bfe used in calculations, this being the only heat liberated ^*n the cylinder. INTKBNAI/-COMBUSTION ENGINES. 99 Volume in cu. ft. Weight in lbs. Specific Heat. B.T.U. (Low). 116.28 430.83 99.35 24.02 Air.cu. ft. for k,. k^. complete Combus- tion. H .3978 .4516 .0638 .0704 .0108 .0050 .00222 .02010 .00496 .00547 .00132 .00039 .1553 .2738 .0477 .0278 .0059 .0020 .2191 .3455 .0580 .0392 .0083 .0003 .967 4.362 .925 .170 669.48 6.424 1.0000 .03451 .5127 .6732 A;p-i-Art> = 1.313 = 71. If a 10 ■ 1 mixture of the above gas be used in an engine the calcula- tions are as follows: 1 cu. ft. of mixture (10 vols, air + l vol. gas) weighs [(.0801 IX 10) + .03451]-*- 11 = .07596 lb. Specific heat, A;» = .1832; /fcp=- .2553; kp-i-kv^n = 1.394. Heat required to raise one cubic foot 1 degree F. = .013916 B.T.U. = A. Heat evolved by combustion of 1 cu. ft. of mix- ture = 60.862 B.T.U. = H. // -s- A - 4,374o F. abs. The efiSciency of combustion of coal-gas has been experimentally deter- mined to be as follows: Ratio of mixture 6: 1 8 1 10: 1 12. 1 Efficiency, x 465 .543 .575 .580 The rise of temperature due to explosion at constant volume, R = Hx-t-h, in this case = 4,374 X. 575- 2,515*' F. If this mixture be compressed from 15 lbs. absolute to 80 lbs. absolute, in a common or non-scavenging engine, (a + c)-!-c = 3.51, s = 2.51c, »-f-c'=2.51, and c-*-» = .4. Subitituting these values in the preceding formulas, 7' = 629''F., 3rc = 956° F.. T*- = 2,753*' F., 3rr= 1,860" F. P« 15 lb., Pe=80 lb., P« = 231 lb., Pr-47.86 lb. (^ taken = 0.9«). For a scavenging engine, 7 = 601° F., Te = 914'* F., Te = 3,429® F., rr = 2,315*>F. Pe = 300 lb., Pr = 62.3 lb. (All pressures and tempera- tures are absolute.) The Diesel Enslne. aearance= 0.0625 to 0.07 X vol. of cyl. Com- pression: PV^-^=^C', expansion: PV^-^ = C. Temperature at the end of compression to 500 lbs. pressure = 720° F. ; temperature at the end of combustion = 1,922° F. A test by Mr. Ade Clark in Maroh, '03, showed a consumption of 0.333 lb. of Texas fuel oil (19,300 B.T.U. per lb.) per I.H.P., or 0.408 lb. per B.H.P. and an efficiency of 32.3%. Various Enelne Performances. Koerting engine, 900 H.P., 28% efficiency on BTH.P. (33.5% eff. I.H.P.). A Diesel engine of 160 H.P. tested by W. H. Booth used 0.45 lb. of heavy fuel oil per B.H.P. A Crossley engine using producer-gas required from 0.65 to 0.85 lb. anthracite per B.H.P. A Hornsby-Akroyd oil engine showed a consumption of 0.785 lb. of crude Texas oil per B.H.P. Design and Proportions of Parts. The following matter is condensed from an artisle by S. A. Moss, Ph. D., in Am. Mach., 4-14-04. The results have been derived from 76 single-acting engines (5 to 100 H.P.) made by 20 builders and will serve as an index of average practice Maxi- mum explosion pressures varied from 250 to 350 lbs. per sq. in., and 300 lbs. has been taken as an average. Compression varied from 50 to 100 lbs. (50 for gasoline, 100 for natural gas) and 70 Ihe. has been taken as an average. Maximum H.P. was found to be about 1.125 X rated H.P. Mechanical efficiency about 80%. Values to the right, in brackets, are taken from Roberts' Gas- Engine Handbook. Diam. of cylinder in ins =d. Thickness of cylinder wall, t =Tg-H0.25 in. [t=-0.09d]. •• jacket •• =0.6/ U = 0.045d]. •• water jacket =1.25< U^O.ld] 100 HEAT AND THE STEAM ENGINE. No. of cylinder-head studs — 0.66d+2. External diam. of studs •^d-*- 12 (average). Length of stroke I — 1 . M " " connecting-rod, c =-2.51 *' Weight of piston, w in lbs — 1.3a (a=»area of cyl. in sq. in.), •• '* connecting-rod «>i =0.8a. * * " reciprocating parts {w 4-0.5ti?i). = u>20 ; tuj average — 1.7. Length of piston trunk = 1.5d (average). Bearing pressure on piston due to weight —0.89 lb. per sq. in. Thickness of rear wall of piston =d-HlO. Wrist-pin, diam «=0.22d; length- 1.75 X diam. Diam. at mid-section of connecting-rod . —0.23d. Crank-pin: length— 0.39(2; diam.=0.41d. Oank-throws: thickness -0.26d; breadth— 0.56d. Diam. of crank-shaft, s— 0.375d. Main bearing, length =0.85d (bearing pressure averages 125 lbs. per sq. in.). Fly-wheel: outside diam = 12,300 -«-iV(iNr-r.p.m.). weight in lbs =33.000 X H.P. +N. Revs, per min. N =800-*-Vr[iNr = 380 + (B.H.P.)o-n for 4-cyole. increase t f or 2-cycle.] Piston speed, ft. per min. . . . = 133 v^T Exhaust pipe diam — . 2Sd. •♦ valve " =0.3d rd.35d]. Inlet " *• =0.27d [0.316d]. Gas pipe . " -O.lld. " valve •• -=0.15d. Air pipe '* -0.25d. Max. B.H.P.-da/iV-*- 14,400. [For gasoline, divide by 18,000 (4.cycle) or by 13.500 (2-cycle).] M.E.P.— 60 to 86 lbs. per sq. in.; average, 70 lbs. Speed of exhaust gases — 5,200 ft. per min. (average). " ** inlet charge . =6,400 " " " ** "gas =3,700 *• " " •• "air =6,900 " " " Dr. Lucke (in "Gas-Engine Design," D. Van Nostrand Co.) states that engines should be designed to withstand max. pressures of 450 lbs. per sq. in The following additional formulas are taken from his work: Thickness of cylinder wall, < = (.062 to .075 )d +0.3 .in. Wrist-pin: diam.=0.35d, length =0.6<f. Piston rings- number = 3 to 10, width— 0.25 to 0.75 in., greatest radial depth =0.02rf+ 0.078 in. (Gttldner), or, =0.033d+0.125 in. (Kent). Valve diam., i; = (0.3 to 0A5)d; valve-stem diam. = (0.22 to 0.3)t>; valve lift — (0.05 to l)t; for fiat valves, — 50% greater for 45° conical valves; valve- seats, width = (0.05 to 0.1)t>; valve-f aces = ( 1 . 1 to 1.5) X width of seat, for conical valves. The following additional data are taken from E. W. Roberts' Gas-Engine Handbook l(tor two-cycle) — d to 1.25d; diam. of water-pipes = 0.15d; diam. of fly-wheel hub = 2«; hub length — 1.75« to 2.25«; mean width of oval spoke or arm = 0.8s to 1.2«; mean thickness of arm — (0.4 to 0.5) X mean width: number of spokes = 6 (generally). Engine Foundations. In order to absorb the vibrations of an engine it should be bolted to a foimdation whose weight F is not less than 0.21jEVjv, where ^ = wt. of engine in lbs. Brick foundations weigh about 112 Iha. per cu. ft. and those of concrete about 137 lbs., an average being about 125 lbs. per cu. ft. Number cu. ft. in foundation = F -j- 125. The inclination or "batter" of the foundation walls from top to bottom should be from 3 to 4 in. per foot of height (E. W Roberts). AIB, Air is a mechanical mixture of oxygen and nitrogen, — 21 parts oyxgen + 79 parts nitrogen, by volume (23 parts 0+77 parts N, by weight). 1 cu. ft. ot pure air at 32° F. and at a barometric pressure (B) of 29.92 inches of mercury (14.7 lbs. per sq. in.) weighs 0.080728 lb., and the vol- ume of 1 lb. — 12.387 ou. ft. At any other temperature and preanm. t AIB. 101 . , ^ *x 1.33021? 2.707P , « u • vx t weU^t per cu. ft., u>=--7^^-r- - t^^-t^, where B— height of meroury 461 + < 4ol+< in barometer in in., <= temperature in degs. F., 1.3302— weight in lbs. of 461 cu. ft. of air at 0^ F. and 1 in. barometric pressure. Air expands lis of its volume for each increase of 1° F., and the voliune varies inversely as the pressure. Air liquefies at —220° F. (its critical temperature) under a pressure of 573 lbs. per sq. in. and boils at —312** F. Specific gravity at — 312**F. =-0.94. Latent heat = 123 to 144 B.T.U. per lb. Liquid air occupies about B^v of the volume of the same weight of free air at normal tem- peratures. Barometric Determination of Altitudes. Pressure of the atmos- phere at sea-level (32° F.) = 14.7 lbs. per sq. in. Difference of levels (at 32** F.) in feet = 60,463.4 log -g (1), where B and Bi are the barometric readings of the two levels. If B is taken at sea-level it is equal to 20.02 in. and Height above sea-level = 60,463.4 log=^ (2). For any other temperatures, t (for B) and h (for Bi), formulas (1) and (2), must be multiplied by a correction factor, c = H-0.00102«-|-/i-64). Approximately, the pressure decreases 0.5 lb. per sq. in. for each thou- sand feet of ascent. Flow of Air in Pipes. Q, in cu. ft. per min. "cY^^, where j>— differ- ence between the entering and leaving ^au^ pressures in lbs. per sq. in., d^diam. of pipe in in., L— length of pipe m feet, and w= density of the entering air (lbs. per cu. ft.). When <i=i in. 2 in. 3 in. 4 in. 9 in. 12 in. e=45.3 52.6 56.5 58 61 62 Richards' formula is Q - lOOT ^i^. When (2=1 in. 2 in. 3 in. 4 in. Sin. 12 in. O-0.35 0.565 0.73 0.84 1.125 1.26 Fl ow of Air throug h Orifices. The oretical velocity in feet per see. r-r 2(^X27.816(1-^) = l,337.7ri-~. where p is the pressure in the reservoir out of which the air flows, and Pi the pressure of the receiving- reservoir. For the actual efflux the value of v must be multipUed by the proper one of the following coefficients . Pressure (in atmospheres). 0.1 0.5 1 5 10 100 Orifice in thin plate 0.64 0.57 0.54 0.45 0.436 0.423 *• , short tube 0.82 0.71 0.67 0.53 0.51 0.487 Loss of pressure, p =• 0.107vhvL + c^d, where to at ordinary temps. = 0.03(pi-*" 14.7)"*'*, Pi (at entrance, absolute) and p both in lbs. per sq. in. COMPRESSED AIB. Free air is that at atmospheric pressure and at ordinary temperatures (14.7 lb. per sq. in., 62** F.). Absolute pressure-gauge pressure + 14.7 lb. Absolute temperature =461** F.-t- reading of thermometer in degs. F. Relations between Temperature, Volume, and Pressure. PV=/2t; JJ-53.354; P=^ap. In the foregoing p, V, x, and Pi, Vu are the respective initial and final absolute pressures, volumes, and bsolute temperatures. Work of Compression. Ft.-lbs. of work required to compress 1 cu. Pi ft. of free air to any desired pressure, pi, isothermally — 144pXlogc— . Ti are absolu 102 HEAT AND THE STEAM ENGINE. If p — 14.7 lb., work in H.P. =0.0641 log<?~^, when compressed in 1 min. Ft.-Ibs. of work required to compress 1 lb. of free air adiabatically at the absolute temperature t, '=(Ti-T)X778X0.2376 = 184.7(Ti-r) ft.-lbs. iifY"-^]- — 184.7 T I (—) — 1 I » where n is the temp, correspondingr to the volume to which the air is compressed. For work to compress 1 cu. ft. divide above value by the number of cu. ft. in 1 lb. at r. In practice the actual work = work of isothermal compression + about 60% of the difference between isothermal and adiabatic work. The Output of a Compressor at any Altitude expressed in per cent - 100 - 0.0028 X height in feet (approx.). Loss by Cooling varies from 70% under bad conditions to 20% with reheating and air injection. lioss by Pipe Friction per mile =5%. Reheating. Gain by reheating in per cent = 100 (l — ^), where t and Ti are the absolute temperatures before and after heating. Tests made at Cornell University bhow that from 28 to 38% min in thermal economy can be made by reheating air from 90° to 320** F., the efficiency of the reheater being 50%. There is no additional gain made by heating above 450° and ii 300° is much exceeded there is danger of charring the lubricant. Pneumatic Tools (cu. ft. of free air required per min., 80 lbs. pressure). Chipping and calking tools, 11 (light) to 17 (ho&vy): riveting tools. 15 (i in. rivet) to 22 (U in. rivet): drills (metal), 15 (1 in.) to 35 (3 in.); wood-boring, 12 (1 in.) to 18 (2i m.). FANS AND BLOWEBS, Let fc = pressure generated in inches of water (1 in. water ■-0.677 os. per sq. in. 1 os. per sq. in. = 1.73 in. water); v= peripheral velocity of wheel in ft. per sec; vi = velocity of air entering the wheel through the suction openings in side of case (25 to 33 ft. per sec); e{=»diam. of suction openings in in. (for openings on bo th sid es of wheel, d= 1^.54 Vg-T-2ri; for opening one side only, d = 13.54V^g-Ht>i); JDj — inner diam. of wheeled to l.5d; D — outer diam. = 2Z)i for suction -fans (=3i)i for blowers); JV = r.p.m. = 229r-*-D; 6 = width of vanes at 2)i = 0.25d to 0.4d for suction opening on one side ( — 0.5d to 0.8d for openings on both sides); &i = width of vanes at Z), =6i>i-»-2>; No. of vanes =0.376I>; q—cu. ft. of air per sec; i;=efficiencv=0.5 to 0.7 for large fans (0.3 to 0.5 for small fans); e = 1.2 to 1.4 for large fans (1.4 to 1.7 for small fans); a = angle which the extreme outer element o f a vane makes w ith the radius at that point. Then, i;=3.28[4 tan o + v^(4 tan a)2-|-200A]. a is positive when the vanes are curved or inclined backward from the direction of rotation (ne gative when forward). For radial vanes a=0, and v = 46.4c V^A™ 46.4 Va + 9. Area of discharge-opening in sq. in. = 144 q-i-vs, where V2= velocity of air in pipe in ft. per sec. H.P. required =5A-«- 106. 7^. Outer diam. of disc fan in in.=3V<jy i»=0.2 to 0.3. MECHANICAIi BEFBIGEBATION. Mechanical refrigeration is produced by expanding a heat medium from a normal temperature to one which is below the usual limits for the climate and zone where the expansion takes place. Media are chosen with regard to their willingness to surrender their heat energy to surround- ing objects, and vapors are therefore best employed. The vapor chosen is compressed and then relieved of its heat in order to diminish its volume. It is then expanded so as to do mechanical work and its temp>erature is lowered. The absorption of heat at this stage by the vapor in resuming its original condition constitutes the refrigeratincr effect. MECHANICAL REFRIGERATION. 103 Ammonia (NH3), Sulphur dioxide (SO2), Pictet fluid (S02+3% of car- bonic acid, CO2) and air are most employed, ammonia and air being of principal importance. Air is used on shipboard where pungent vapors would be objectionable. (V,\ 0.41 /p X 0.29 T ■y-j = ( — ) = — . Air is cheap and harmless, but its use is limited on account of its bullc and the size of the machinery employed. Efficiency, measured in ice-melting effect (latent heat of fusion of ice » 142.2 B.T.U.) is between 3 and 4 lbs. of ice-melting capacity per lb. of fuel, assuming 3 lbs. of fuel per H.P. Saturated Ammonia is inexpensive, remains liquid under atmospheric pressure only below —30° F., and at 70° F. under 116 lbs. gauge pressure. Properties of Saturated Ammonia. Temp. Degs.F. Abs. Pres- sure, Lbs. per Sq. In. Heat of Vaporization, B.T.U. Vol. of Vapor. Cu. Ft. per Lb. Vol. of la quid. Cu. Ft. per Lb. Wt. in Lhfl. of 1 Cu. Ft. of Vapor. -40 10.69 579.67 24.38 0.0234 0.0411 -30 14.13 573.69 18.67 .0237 .0535 -20 18.45 567.67 14.48 .0240 .0690 -10 23.77 561.61 11.36 .0243 .0880 30.37 555.5 9.14 .0246 .1094 flO 38.55 549.35 7.20 .0249 .1381 20 47.95 543.15 5.82 .0252 .1721 30 59.41 536.92 4.73 .0254 .2111 40 73 530.63 3.88 .0257 .2577 50 88.96 524.30 3.21 .0261 .3115 60 107.60 517.93 2.67 .0265 .3745 70 129.21 511.52 2.24 .0268 • .4664 80 154.11 504.66 1.89 .0272 .5291 90 182.8 498.11 1.61 .0274 .6211 100 215.14 491.5 1.36 .0277 .7353 Ammonia Compression System. The ammonia vapor is compressed to about 150 lb. pressure and a temp, of 70° F., and is then allowed to flow into a cooler or surface-condenser, where the heat due to the work of compression is withdrawn by the circulating water and the vapor is condensed to a liquid. It is then allowed to pass through an expansion cock and to expand in the piping, thereby withdrawing heat from the "brine" with which the pipes are surrounded. This brine is then circu- lated by pumps through coils of piping and produces the refrigerating effect. The expanded ammonia-gas is then drawn into the compressor under a suction of from 5 to 20 lbs., thus completing the cycle of operations. The brine consists of a solution of salt in water. Liverpool salt solution weighing 73 lbs. per cu. ft. (sp. g. = 1.17) will not congeal at 0° F. Amer- ican salt brines of the same proportions congeal at 20° F. Ammonia required =0.3 lb. per foot of piping. Leakage and waste amount to about 2 lb. per year per daily ice capacity of one ton. The brine should be about 6** colder than the space it cools. Ammonia Absorption System. In this svstem the compressor is replaced by a vessel, — called the absorber, — where the expanded vapor takes advantage of the property of water or a weak ammoniacal liquor to dissolve ammonia-gas. (At 59° F. water absorbs 727 times its own volume of ammonia- vapor.) The liquor in the absorber is then pumped into a still heated by steam-pipes, where the ammonia-gas is vaporized, the remainder of the process bein^ then the same as in the compression system. The absorption system is less expensive to install, and com- mercial ammonia hydrate (62% water, sp. g. =0.88) may be used in the absorber. Efficiency. Ice-melting capacity per lb. of fuel=tp»<-7-142.27r, ; Ice- melting capacity in tons (2,000 lbs.) per day of 24 hours -= 24 1/«< -i- (142.2X2,000), where to = lbs. of brine or other fluid circulated i^er hour 104 HEAT AND THE STEAM ENGINE. «ri»lbfl. of fuel used per hour, « = specific heat of the circulating fluid, and t » range of temperature experienced by the circulating fluid in degs. F. Design of a Compression Machine. The weight of the medium required is determined by the condition that each pound must withdraw from the brine the heat necessary to change the liquid medium in the condenser at t (with a heat of liquid in each lb. = h) into saturated vapor at ti in the vaporizer, where the totid heat of evaporation per lb. = H. The heat withdrawn per lb. per min., L = H — h^ and, in ice made per hour, the weight of the medium, to = 142.2Xlbs. of ice made per hour-i-60{H — h). Assuming the compression to be adiabatic, the absolute temperature of the superheated vapor leaving the cylinder, jP« = 22( — ) • where T2 is the absolute temperature (degs. F.) of the vapor in the expansion or vaporizer coils in the brine, and Pi, P2 are the pressures before and after expansion. The cooling water required in the condenser, W = uikp((a — ti) + H — h] lbs., where A;p = specific heat of the superheated vapor at constant pressure, t8 and <i "= temperatures (F.) of the compression cylinder and condenser respectively, and (H— A) = heat of vaporization at tne pressure Pi of con- denser. The H.P. of the steam cylinder driving the compressor where Hi and H2 are the total heats of vaporization at the pressures and temperatures in the condenser and vaporizer, respectively. This value must be increased to allow for heat and friction losses. ~™ , , ^, ,. J tt?Xvol. of 1 lb. of vapor The volume of the compressor cylmder = -T;: r- ; ^ — • No. ot strokes per mm. Specific Heats at Constant Pressure (kp). Ammonia, 0.508; car- bonic acid, 0.217; sulphur dioxide, 0.1544. Temperatures for Cold Storage. Fruits, vegetables, eggs, brewery work, 34" F.; butter, cheese, shell oysters, 33° ; dried fish, canned goods, 35°; flour, 40**. The following should be frozen at the first temperature and then maintained at the second: Butter, 20°, 23°; poultry, 20°. 30°; fresh fish. 25°, 30°; tub oysters, 25°; fresh meat, 25°. HEATING AND VENTILATION. Ventilation. Impurities in air are due to carbonic acid and organic particles exhaled from the lungs, water vapor from perspiration, dust, smoke, noxious gases, etc. The measure of impurity, however, is taken as the content of carbonic acid, which should not exceed 6 to 8 parts in 10,000. Fresh air contains 4 parts (country air, 3 to 3.5) in 10,000. The hourly yield of CO2 per person is 0.6 cu. ft.; consequently each 1,000 cu. ft. of fresh air can tal% up at least 0.2 cu. ft. of CO2 and not exceed the limit of 6 parts in 10,000; hence 3,000 cu. ft. of fresh air per person, if uniformly diffused, will keep the respiratory CX)2 down to that limit. It is further found that the atmospheric contents of a room may be changed three times per hour without 'causing inconvenient draft, hence 1,000 cu. ft. of air space is a proper provision per person. From 2,000 to 2,500 cu. ft. per person per hour is sufficient for auditoriums used but for two or three hours at a time. School-rooms should have at least 1,800 cu. ft. per scholar per hour, and in hospitals from 4,000 to 6,000 cu. ft. per patient per hour should be suppUed on account of the various unhealthy excre- tions. According to Bietschel (Ing. Taschenbuch) the hourly supply of air per capita in cubic feet should be as folio .vs Hospitals, adults, 2,600, — chil- dren, 1,200; schools, pupils under 10 yrs., 400 to 600, — pupils over 10 yrs., 600 to 1,000; auditoriums, 600 to 1,100; work rooms, 600 to 1,100; living rooms, 1 to 2 times cubic contents; kitchens and closets, 3 to 5 timen cubic contents. Carpenter states that the number of changes of air per hour should be as follows Residences, — halls, 3; living rooms, 2; sleeping rooms, 1. Stores and offices, 1st floor, 2 to 3; upper floors, 1.5 to 2. Assembly rooms, 2 to 2.5. HEATING AND VENTILATION. 105 Heatins of Buildings. Let W^sq. ft. of transmitting surface, <i"- inside temperature, <2 = outside tempefature, both in degs. F. <=-<i— ^, ^ = a coefficient representing for various building materials the heat loss by transmission per sq. ft. of surface in B.T.U. per hour for each deoree of difference of temperature on the two sides of the material, and « — the total heat transmission = PT/c^ Values of k (Ing. Taschenbuch). Thickness of wall in inches •. . . . 4 8 12 16 20 24 28 32 36 40 48 i% for brick 0.53 .38 .30 .25 .22 .19 .17 .15 .13 .12 Do. sandstone 0.45 .39 .35 .32 .29 .26 .24 .22 .19 For limestone add 10% to values for sandstone. Solid plaster partitions: 1.75 to 2.25 in. thick, 0.6; 2.5 to 3.25 in., 0.48. Floors, joists with double floors, 0.07; stone floor on arches, 0.2; planks laid on earth, 0.16; planks on asphalt, 0.2; arch with air-space, 0.09; stones laid on earth, 0.08. Ceilings- joists with single floors, 0.1; arches with air-space, 0.14. Windows: single, 1.00; double, 0.46. Skyhghts single, 1.06; double, 0.48. Doors, 0.4. The above values should be increased according to conditions as follows: For rooms unusually exposed, add 5%: for N., NE., E., NW. and W. exposures and where height of ceiling (h) exceeds 18 ft., add 10%; for h=13 ft., add 3i% : for h^ 15 ft., add 6^%. For rooms heatea daily, but not at night, add A=0.0625 (N^l)H-i-Z; and for rooms not heated every day, add B = 0.1(8 +Z)H-i-Z, where JV=- No. of hours between cessation of heating and restarting of fire, and Z — No. of hours from starting of fire until rooms attain required temperature. In heating assembly rooms account must be taken of the heat givjen out by audiences and illuminants. A person gives out about 400 B.T.U. per hour, an ordinary gas-burner about 4,800 B.T.U. per hour, and an incandescent electric lamp (16 c. p.) 1,600 B.T.U. per hour. A gas-burner vitiates the air as mucli as 5^^ persons. B. T. U. pep Hour required to Heat a Boom. (Carpenter.) No. of B.T.U. = (rg-4-0 + --rJ^ where n = No. of changes of air per hour, C — cu. ft. in room. G^^sq. ft. of glass, W==sq. ft. of wall surface exposed to outside air, and indifference between inside and outside temperatures in degs. F. Radiation. Ordinary bronzed cast-iron direct radiators give out about 250 B.T.U. per hour per sq. ft. of radiating surface, with steam of 3 to 6 lbs. pressure. Unpainted radiating surfaces of the ordinary in- direct type give out about 4O0 B.T.U. per sq. ft. per hour. For hot-water heating 60% of these values may be taken. Hot-air furnace walls transmit about 600 B.T.U. per sq. ft. per hour if the walls are much extended, and about 800 B.T.tl. if the surfaces are smooth, air temperatures at registers being from 100° to 150° F. Boilers when coal-fired will transmit 2,500 to 4,000 B.T.U. per sq. ft. of heating surface per hour, and from 4,000 to 5,000 B.T.U. when coke-fired. Hot- air systems provided with blowers yield transmission values up to 2,000 B.T-U. per sq. ft. per hour. Approximate Heating Values of Radiating Surfaces. One square foot of radiating surface will heat by direct steam radiation- Dwellings, school-rooms, offices, 60 to 80 cu. ft. ; halls, lofts, stores, factories, 75 to lOO cu. ft.; churches, large auditoriums, 150 to 200 cu. ft. For direct high-temperature hot-water heating, take I of above values, — for low- temn. hot-water heating, take i of same. For indirect radiation, take } of the value for direct radiation. Siscs of Pipes for Steam-Heating. (Wolff.) Allow 0.375 sq. in. sectional area per 100 sq. ft. of radiating surface tor exhaust-steam heat- ing, 0.19 sq. in. per 100 sq. ft. when live steam is used, and 0.09 sq. in. per 100 sq. ft. for returns. Each horse-power of boiler capacity will sup- ply from 80 to 120 sq. ft. of radiating surface. ("Steam.") In stood hot- water boilers, the ratio between grate area, boiler heating surface, and radiating surface is 1 : 40 . 2(X). J HYDRAULICS AND HYDRAULIC MACHINERY. Water (1 part H+8 parts O.) Degs. F. Lbs. per cu. ft. Relative Vol. Degs. F. Lbs. per cu. ft. Relative Vol. 32 62.418 1.00011 100 62.02 1.00686 39.1 62.425 1.00000 120 61.74 1.01138 50 62.41 1.00025 140 61.37 1.01678 60 62.37 1.00092 160 60.98 1.02306 62 62.355 1.00110 180 60.55 1.03023 70 62.31 1.00197 200 60.07 1.03819 80 62.23 1.00332 210 59.82 1.04246 90 62.13 1.00496 212 59.76 1.04332 For sea- water, multiply above weights by 1.026. Pressure Equivalents. 1 ft. water at 39.1° F. (max. density) = 62.425 lbs. on the sq. ft., « 0.4335 lbs. on the sq. in. = 0.0295 atmospheres on the sq. in. 1 lb. on the sq. ft. at 39.1<» F. =0.01602 ft. of water; 1 lb. per sq. in. « 2.307 1 atmosphere (29.922 in. mercury) =33.9 ft. of water. 1 ft. of water at 62° F. (normal temp.) = 62.355 lbs. per sq. ft. =0.43302 lbs. per sq. in. 1 inch of water at 62° F. (normal temp.) = 0.036085 lbs. per sq. in. Hydrostatic Pressure. The pressure of a Uquid against any point of any surface upon which it acts is always perpendicular to the surface at that point, and, at any given depth, is equal in all directions and due to the weight of a uniform vertical column of liquid whose horizontal cross- section is equal to the area pressed upon and whose height is the vertical distance from the center of gravity of the surface pressed to the surface of the liquid. . , . , , , , When a liquid pressure is exerted on one side of a plane area, the result- ant force experienced by the area is perpendicular to the area, equal to the sum of all the pressures and acts at a definite point called the center of pressure. Centers of Pressure A(= vertical depth from surface of liquid). Rectangle : upper side parallel to liquid surface and distance ^i from { Triangle: base lying in surface of liquid, h surface, base horizontal, h = 3a-*-4. ^— 3-- Circle or Ellipse : h = a + hi + 4(a + Ai)' 2; vertex in Uqidd if ht^O, h^5a+4. 106 HYDRAULICS AND HYDRAULIC MACHINERY. 107 In the above a = vertical height of triangle or rectangle, radius of circle or vertical semi-axis of ellipse. Buoyancy. When a body is immersed in a liquid it is buoyed up by a force equ£kl to the weight of the liquid it displaces whether floating or sinking. This upward pressure may be considered as acting at the c. of g. of the displaced liquid, or, as it is termed, at the center of buoyancy, and a vert, line drawn through the center is called the axis of flotation. The line connecting the center of buoyancy and the c. of g. of a floating body at rest is called the axis of equilibrium and is vertical. If an external force acting on the body inclines the axis of equilibrium, a vertical line from the center of buoyancy intersects this axis at a p<5int called the meta- center. The equihbrium is stable, indifferent, or unstable, according as the metacenter is above, coincident with or below the center of buoyancy. Head, Pressure, and Velocity Energy. The pressure of the atmos- phere balances the pressure of a column of water 33.9 ft, high, and the '•head "of the column, H = 33.9-5- 14.696 = 2.307p. If a vertical gauge- tube be inserted in a pipe the water will rise in it to a height propor- tional to the pressure; then, connecting head and pressure PA^'GHA^ P^GH, and H=P-i-0, where P = supporting pressure in lbs. per sq. ft., fr-» height of column in ft., G^^ weight of 1 cu. ft. of water in lbs., and A -=area of cross-section of column in sq. ft. Head and Velocity. A water particle (weight «= to) at height, H. has a potential energy equal to tc/T, and when it has fallen through It its kinetic energy » -r— . Neglecting friction and other losses, wH « wv^ -f- 2g ^g and © = '^2oH » 8.02 v^. Any given portion of water flowing steadily between two reservoirs which are kept at a constant level will, — neglecting friction and viscosity, — possess an unvarying amount of energy which may be due to head, pressure, velocity, or to all three. If a vertical gauge-tube be inserted at any point of the pipe connecting the reservoirs the water will rise in it to a Idvel below that of the reservoir from which it flows, a portion of the head energy represented by the difference of levels having become kinetic, p and the total head {Ht) consists of H due to unexpended fall + ^ due to pressure (as shown by gauge-tube) 4- g" due to velocity. Multiplsdng each by w gives the respective energy, the energy of 1 lb. P v^ of water being Ht''H-\-^+^. By sufficiently contracting the sectional area of the pipe at some point between the reservoirs the throttling so caused will reduce the pressure below that of the atmosphere and create a partial vacuum. This principle is employed in jet-pumps (efficiencies, 30 to 72%). Discharge of Water through Orifices. If a reservoir is emptied through an orifice near its bottom, the volume of the water passing. Q» velocity X area of orifice, and, neglecting resistances. The Theoretical Dis- charge in cu. ft. per sec. g=»Ar=8.02AVi^. On account of resistances V is reduced, and, letting ci= coefficient of velocity, t;-»8.02ci>/^. if the reduced velocity be considered as due to a loss of head, Hr, a coeffi- cient of resistance, p, may be adopted, Hr being taken as equal to pHu where Hi ia the remaining or unexpe nded head. H=^Hi + Hr'^H\+pHi -^(l+pWi, and r«8.02V^=8.02|/^. Also. ^^^ = 1^7^, ci- A -rp 1 +p 1+P Vx~r~* a^d />— — « — 1. This loss occurs within the vessel and orifice. 1 +p Ci* A further loss is caused by the contraction of the jet area at a distance from the orifice equal to one-half the jet diam. Let A; = coefficient of con- traction ; then. Actual Discharge in cu.f t. per sec. , Qa = CivkA =* 8.02A;A y , or, letting C—CiA— coefficient of discharge, ga'-8.02ACVly, 108 HYDRAULICS AND HYDRAULIC MACHINERY. ATerage Values of Coefficients. Orifices. Sharp-edged. Re-entrant Cyl. Cylinder. Bell-mouthed. 0.97 0.0628 0.64 0.62 1.00 0. 0.53 0.63 0.82 0.487 1.00 0.82 0.99 0.02 1.00 0.99 Measurements of Water-Flow over Weirs. Let a stream be partly dammed and the water allowed to flow through a rectangular notch, or weir, which is beveled to sharp edges on the intake side. To find the discharge, divide the head, H (or distance from edge of notch to surface of water), into small portions, ^i.and consider each small rectangle (Ai Xlength of notch, L) as a separate orifice. At any depth, H\, i; = 8.02V^^ and the discharge through the small rectangle =8.02Lv^^i. Representing the various discharges by horizontal lines of proportionate length, the figure bounding these lines will be found to be a parabola of base "» 8.02L Vw^ and height — head H (the lines varying in length as V/fi). The total theoretical discharge will then be equal to the area of the parabola, or, 3 =• f X8.02Lf^* = 5.347L/79. The actual discharge is smaller, being, according to the following authorities: Both end contractions suppressed. Francis. ..ga = 3.33L/rJ Smith ga = 3.29 One suppressed. 3.33(L-^)Ht (^+f)«' >ss than ZH. a, sharp-creJ ted behind \ qa = [0.425 + 0.21 (jf^) ^S.02LH^, Full contraction. 3.33(1, -0.2ff)^i. 3.2»(L-|)ff«. (L should not be less than SH.) For flow over a sharp-crested weir without lateral contractions, air being freely admitted behind the falling sheet of water, where Hi^ height in feet from bottom of channel of approach to the crest of weir (Bazin). In triangular notches j^ at any depth is constant and therefore C is regular and may be taken as 0.617. go = i*»CL/f?v^ = 1.32L//3. For a 90° notch. L=2^ and q -2.64i?l: for a 60° notch, L = 1.155H and g«=1.624//5. ^^ „ „ * o* Qa XOXH (available height of fall) Tlie Horse-Power of a Stream ='^ ^^ ^^ ■ =0.1135gfl/y. Friction in Pipes is independent of the pressure but is proportional to the wetted surface. FnccAv^='tiAv'^, at moderate velocities, and, as 1.03G^2g, Fn=imfj^A^. If a cylindrical body o. water (length L, diam. D) move at a velocity, V, through the pipe, Fn per aq. ft. of sectional area = 1. 03 fiG or na ' ol J 1}2 ' /, ^^ = 4. 12/r^ X G X ^ , Mid , as fl^ = P -s- (?, the Head Lost in Friction = 4. 1 2Ar=r • —• HYDRAULICS AND HYDRAULIC MACHINERY. 109 /t= 0.004 for clean, varnished surfaces, 0.0075 to 0.01 for pipes, and 0.009 for surfaces of the roughness of sand-paper. Wm. Cox's formula: Friction Head=L(4v2+5v — 2)-^l,000d, where d^ diam. in in. (Pelton Water Wheel Co.). Flow of Water tfarougli Pipes. v = CR^S^. (Tutton.) i2 (hydraulic radius) = sectional area -h wetted perimeter, =*i)-H4 for round pipes when full or half -full; S (slope) = Head -i- length of pipe = sine of angle of incli- nation of pipe. Values of C for various materials: W.I. pipe, 160; new C. I. pipe, 130; used C. I. pipe, 104; lap-riveted pipe, 116; W. I., asphalted, 170; wood-stave pipe, 126; rough, pitted pipe, 30 to 80; brick conduits, 110. Flow of Water Id Open Cfaannels. (Kutter.) where S—fall of water surface in any distance -*- said distance — sine of slope; C= coefficient depending on the character of the channel surface, and having the following values: planed boards, 0.009; neat cement, 0.01; plaster (75% cement), 0.011; rough boards, 0.012; ashlar or brick-work, 0.013; rubble masonry, 0.017; canals, firm gravel, 0.02; canals and riverg in good condition, fairly uniform section, free from stones and weeds, 0.025; same, but with occasional stones and weeds, 0.03; same, in bad condition, many stones and weeds, 0.035; torrents encumbered with detritus, 0.05. Tutton 's formula for pipes may also be used as herewith modified, where C has the values given for Kutter's formula: t? = -^fi*5i. Hydraulic Gradient. Water being discharged from a reservoir through a pipe of uniform diameter, the net head at any point may be found by applying a pressure gauge which will show a loss from total head due to velocity, j; — l-loss due to friction. The friction loss varying directly as the distance from reservoir, a straight line bounds the heights of the various water columns in the gauges and is called the line of virtual slope, or hydraulic gradient. No part of a pipe should be above this line, as the pressure would then be less than that of the atmosphere and the water would tend to separate. Loss by Eddies and Shock. Bends, elbows, valves, and cocks pro- duce frictional resistances to flow in systems of piping, which are com- puted in terms of the head and are to be added to the resistance of the pipe in order to obtain the final discharge. Water discharged into a basin delivers all of its energy as shock, but whenever a sudden change of velocity takes place eddies are formed which absorb energy. When an abrupt contraction takes place, as from a large pipe to a smaller one, the loss of head =0.3'»2^"*" 2g, and for a sudden enlarge- ment of sectional area, loss of head = (vi— 1>2)^-^2^, where Vi and V2 are respectively the velocities in the first and second pipes. t Angles and Elbows. Loss of head = cv^-^2a. Let ^9 = number of degrees of the angle through which the direction of flow is deviated; then, for ^= 20 40 60 80 90 100 120 140 c= 0.046 0.139 0.364 0.74 0.985 1.26 1.861 2.431 Bends* Loss of head = c . j^ • o" * *^ depends on the ratio of the radius of the pipe (0.6D) to the radius of curvature of the bend (R). 0.5D-*-i2= 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00 c= 0.131 0.138 0.158 0.206 0.294 0.44 0.661 0.977 1.408 1.978 Gate- Valves. Loss of head due to partial opening = ct>2-»- 2^. Opening = i i 1 c= 98 17 5.52 2.06 0.81 0.26 0.07 Cocks. Tioss of head = cr2-h2flr. Opening = i i i c-222 62.6 21.1 7*8 A 0.92 0*2 110 HYDRAULICS AND HYDRAULIC MACHINERY. WATER WHEELS. Pressure on Yanes. Force causing momentum =— /, and.aa/— v-s-<, Pt^wv-i-g, or, pressure X time (i.e., impulse exerted) —momentum ated. If <» 1 sec. and t(7»weight of water passing per sec., tov*-g*^> of momentum = P = pressure on vane. Flat Plate or Yane, fixed (its velocity being 0). P^tiw-t-g'^ iOAv)v-^g. Flat Plate Moving In the Direction of Jet. (Vel. of plate »ti2. vel. of jet = vi.) Water passing per sec.^OAivi — vz). /* -= diflference of momen- tum before and after impact, '^[OA(vi — V2)vi-*'g]—[GAivi—V2)v2 + g}^ GA(vi — V2)^-i-g. Moving Hemispherical Surface or Cup. Relative velocity of jet and cup when meeting = i>i — 1;2 (forward), and when leaving, =vi—V9 (back- ward). Consequently, the absolute discharge velocity— cup velocity — relative backward velocity, —V2--(vi—V2)=^2v2 — vi, whence, P=» OA(v,-v,)v, _ OA(v,-v,X^-v,) _ 2QA(v,-v,)' _ If ^-^+2. the abao- g g a lute velocity of rejection =0, and all of the jet energy is exerted on the cup. Wheel with Radial Yanes, a vane being constantly before the 'jet: Momentum before impact, •=(Gi4vi)»i+(7; after, '^iOAv\yo2.-^g\ .*. P«- GAiOx^Vx—Vi) g Wheel with Many Curved Yanes i momentum before impact — QAv^-^g\ after, — (?A©i(2i^— »|)+at •*• P — 2G-4i>i(vi — i;2)+^f or twice that of flat radial vanes. In this case and that of the hemispherical cup the direction of the jet water is returned upon itself- Undershot Wheels are suitable for falls less than 6 feet. Diameter may be 4 X fall. Efficiency; with radial floats or vanes, 30% ; with curved floats, about 65%. Circumferential velocity — 65% of the velocity due to head (approx.). As the floats are never filled with water, the action is due to pure impulse, and if the floats are properly curved the water enters without shock and leaves without horizontal velocity. Construction of float curve (Fig. 23); From the center of wheel draw OA vertically and make ^0^=^15°. Let the jet (of thickness C, — iXhead) have a slope of J in 10. From the middle of jet, Z>, draw DE so that 0DE'^23P. Take D^-0.5 to 0.7 X head, and from B strike the arci>P, which is the curve for the Poncelet form of undershot wheel. lOTtolS* Fig. 23. Breast Wheels are used for falls from 6 to 12 feet. Efficiency from 60 to 65%. Vanes curved similarly to those of Poncelet wheel. TURBINES. Ill Overshot Wheels are used for falls ranging from 12 to 70 feet. Effi- ciency, 70 to 75%. Best circumferential velocity- 6 ft. per sec. —one-half the velocity of the water due to a fall of 2.25 ft.; conse.quently, point at which water strikes wheel should be 2.25 ft. below the' top water level. Construction of float curve (Fig. 24): make ED^AB'*-d, and 'BC-'1.2AB. Draw CO 10** to 15** to radius. From O strike the arc FC, F being Hear to Z>, and round the arc curve into radial line DE. The Pelton Wheel is used for heads exceeding 200 feet. In it the water in the form of a jet impinges on a series of cup-shaped buc kets affixed to the wheel circumference, to which latter the direction of Jet is tan^ntial. These cups are made double, with a center fin which splits the jet and returns the water on the sides, the discharge being effected with but little velocity. Efficiency, from 80 to 90%. Bucket velocity should be one- half jet velocity. TURBINES. Turbines are water wheels in which the motion is caused by the reaction of the water pressure between stationary guide blades and the vanes or floats of the wheel. The water flow may oe axial or radial (inward or outward) in direction, and it should be sp deviated that it enters the wheel floats as nearly at a tangent as possible, and leaves either radially or in a direction parallel to the axis as the case may be. Kadial Outward-Flow Turbines (Foiunejn-on type). Q'^cu. ft. water passing per sec. under a head of H feet. Inner radius i2i-«0.326V^; outer radius R'^cRu where c^l.25 to 1.5. Angle of guide at entrance o-=15*> to 30^ Angle of bucket at same point, /?=»2a + 20° to 30**. The velocity of wheel at Ui =t>i — a/ 2 sin ^ cos a -.^[(.J^)'-']' sin i0—a) (If a = 15°, i9 = 60». c=1.6, Vi^4.sWh.) Velocity at i? = » — cri ; r.p.m. = GOv + 27rR = 9.55i> + R. Velocity through guide passages, »2 = t>i sin ff-i-sm(a—0). Area of cross- section of all openings = Q+tr2 =-4 -=Q 8m(a—0)+Vi sin 0. If Z>= depth and B = width of a bucket, i>-»-B=-A = 2 to 5, inversely according to the head of water. Thickness of metal floats, T*— 0.015i2. D^jr-s^^^ri+(^-^^^^^^^)\ Number of guides, -Yi=M+i>2. No. of wheel buckets, N^Niain 0-i-8ina. Angle of discharge, 9: sin^ — {Ai+NTD)-^2nRD, where ili — area of discharge openings. Cxirvature of floats (Fig. 25): Draw CAB =^8, drop QB perpendicular to AS. AD = i4^ = 5-1-2. Set off BF and BO^AD, From F strike the are HD. Draw DK = CL, making BDK ~ 180"* -0, and join CK. Bisect CK at M and draw the perpendicular MN, Draw arc DL from iNT as a center. Draw PL and CP, each inclined to CL by a**. From P as a center strike the arc RL of guide blade. Inward-flow turbines are designed similarly, but in an inverse manner. Axial or Parallel-Flow Turbines (Jonval type). The guide blades in this type are arranged in the form of a ring above the wheel vanes, the water flowing parallel to the axis. These wheels work best when sub- merged in the tail-race or connected thereto by a draft-tube whereby the suction of the latter may be availed of. a =15° to 25°, i9 = l(X)° to 120°. Velocity, v, same as velocity vi of the Foumeyron wheel where c= 1. Veloc- ity of entering water = »i =» sin 0-i-sin(0—a). Total sectional area of en- trances between guides, A =Q-i-vi; total discharge area, ili'^Q-t-v. Mean radius, /2 = ( i?i + /Zg) -^ 2 ; radial width of operative ring of wheel, D-» R^-Ri-^OAR, an d R^^O.S R; R2=l.2R. i = D^5 = 2to4. «, approx. = r ;r-^ — : — ; r= 0.02ft. No. of guides, -ATi » (A -»- BD) + O.ojT sm a (XA +D^ : No. of floats, N^Nx sin -^ sin a. Sin ^ = (Aj + NTD) + 2kRD. R.p.m. = 9.55t;-+-i2. Height of wheel = (0.5 to 0.%)R. Chirvature of floats (Fig. 26): Both the guides and floats are warped surfaces generated by a line at right an^es to the axis, whose outer end 112 HYDRAULICS AND HYDRAULIC MACHINERY. follows the curves in the figure. Draw AB inclined to the plane of wheel by a°, and similarly DC at d°. Draw BF perp. to AB, From F as a cen- Fig.25. Fig. 26. ter, strike the arc BE. Draw D(7 perp. to DC, make angles ODA ='DAG = {P+9)-i-2, and from intersection &, as a center, draw arc DA. The lower parts of guide and float {AB and CD) are straight lines. Impulse Turbines (Girard type) are parallel- flow wheels with the wheel passages so enlarged toward tne outlet and ventilated that they are never entirely filled with water, the energy being purely due to velocity. They are regulated by entirely closing a number of the guide passages, the efficiency (60 to 80%) being therefore unimpaired by fractional open- ing. Modem Practice. (From articles by J. W. Thurso in E. N., Dec., *02.) For heads less than 20 ft., use radial-inflow reaction (Francis) turbines with vertical shafts; for heads of 20 to 300 ft., the same, but with horizontal shafts; for heads exceeding 300 ft., use radial, outward-flow, free-devia- tion turbines with horizontal shafts, or Pelt on wheels. Parallel-flow turbines are now largely abandoned on account of their poor regulating qualities. Free deviation may be obtained with an eflS- ciency of 70% at 0.2 gate, and 80% at full gate; reaction turbines with 60% efficiency at 0.2 gate and 78% at full gate. (Highest eff., 80% between 0.8 and 0.9 gate.) Reaction wheels are either regulated by making the guide- vanes mov- able, so that the openings may be reduced according to Toad and without materially altering the direction of flow, or, the guide and wheel vanes are divided by crowns into three or more superposed turbines, any number of which may be shut oflF by a cylindrical gate according to load, allowing those in operation to work at full gate and at the correspondingly higher efficiency. Free-deviation turbines to attain high efficiencies must work in the free air, and, in order to obtain the advantages of draft-tubes, they must be supplied with air-valves which will automatically keep the water-level below and clear of the wheel. -Draft-Tubes. The use of draft-tubes permits turbines to be mounted on horizontal shafts and also to be set above the tail-water without loss of a part of the head. The hanging water-column in the draft-tube is bal- anced by atmospheric pressure and could theoretically attain a height of 34 ft. if the water were at rest, — but, with the water in motion, it cannot exceed (34 — g") ft'» where t; = velocity of water in ft. per sec. When PUMPS. 113 leaving the draft-tube v should not be less than 2 ft per 8ec. when starting at full capacity, not less than 3 ft. per sec. for variable loads over half capacity, and from 4 to 6 ft per se^. for widely fluctuating loads at times of small capacity. The a bsolute velocity of the water issuing from wheel in ft. per sec, Vi^c^2gH, where c = 285 for large turbines and low leads (10 ft.), 0.2 for medium turbines and heads flOO ft.), and 0.167 for small turbines and high heads (500 ft ) // = total nead in feet. When /f = 10 ft., vi = 7.23 ft per sec The head, h^ (due to velocity »i) - 7.232 -4- 2i7 =0.812 It. Let v be the velocity at which water leaves the draft-tube = 3 ft.; the corresponding velocity head. /i = 32-j-2g=0.l4 ft.; the gain in head by asing draft- tube =Ai -A =0.812 -0.14 = 0.672 ft., or 6.72% of H. 75% of this gain should be realized in practice. Under average conditions, the greatest draft head, H permissible for various diameters D of draft-tubes is as follows Z)=0.5 ft., /f = 32.6 ft.; D=8 ft., if = 14.5 ft.; Z) = 9 ft., if = 13 ft. D = 13 ft.. H = 10 ft. From these heads should be deducted h( ^g-} due to velocity, v. of water leav- ing tube. Short draft-tubes of small diam. should extend from 6 to 12 in. below surface of tail- water, — ^long tubes of large diam. from 20 to 24 in. below. Tubes should have a gradual taper, enlarging towards the tail- water, in order to reduce the velocity of the dischai^ and to thus avoid shock. The H. P. of a Water Wheel =(?3//ii + 550, where 9 -efficiency of wheel. As the water has no forward momentum on leaving the turbine (or on entering a centrifugal pump), each lb. undergoes a change of momen- tum =t;-i-^, where v is the forward component of the entering velocity (leaving vel. for centrifugal pump). Let »! = velocity of wheel-nm; then, useful work per lb. water = (Tn>i+(^) ft. -lbs. per sec. —nH, Hish-Elflciency Turbines. Samson (Leflfel) and McO)rmick (S. Morgan Smith &. Co.) turbines tested at the Holyoke flume under heads of about 15 ft. show efficiencies of over 80% at full and f gate, and a maximum of about 85% at i gate. LiORses in Turbines. Surface friction and eddying, 10 to 14% ; energy xejected into tail-race, 3 to 7%; shaft friction, 2 to 3%. PUMPS. Centrifugal Pumps are simply reversed turbines in which the applica- tion of mechanical power to the wheel transforms velocity into pressure and elevates water to the same height (neglecting losses) as the head would be for a turbine running at the same speed. The radial outward- flow type is best adapted for pumping. Water may be raised through suction up to 26 ft., and, using as a force-pump, may be elevated upwards of 100 ft. by well-designed wheels. It is claimed for the Worthington volute type that it will work up to heads of 85 ft., and that tests have shown an efficiency of 86%. A Swiss pump (Sulzer Bros., wheel diam. of 20 in., 890 r.p.m.) tested in 1902, lifted 1,010 gal. (135 cu. ft.) per min. against a head of 428 ft., or, as pump was four-stage, 107 ft. head per wheel. Efficiency, 76%. A single-stage De Laval pump (runner diam. of 13.75 in., 1,545 r.p.m.) driven by a 65-H.P. steam turbine of same make (tested by Profs. Denton and Kent in Apr. '04) lifted 1,760 gal. per min. 100 ft. with an efficiency of 75%. Duty, condensing, 61,860,000 ft. -lbs. per 1,000 lbs. of com- mercially dry steam (moisture <1.7%) and 45,000,000 ft.-lbs. per 1,000 lbs. steam (non-condensing). A two-stage pump of same make (runners 9 in. and 2.84 in. diam., 2,050 and 20,500 r.p.m. respectively) lifted 244 gal. per min. 781 ft. Duty, 48,880,000 ft.-lbs. per 1.000 lbs. steam. Steam ijer water-H.P. (lbs. water lifted per sec. X lift in ft. -4- 550) = 40.5 lbs. i>er hour. Proportions. Ixit 5= wheel radius, and ^i = — =radius of water inlet. Diam. of discharge-pipe, /> = 0..36 v C^-^'*^^^. Diam. of wheel = 2i? = 0.1"' vC' •-*''/. To draw cu-vc of wheel-vane: Let tJi=yelocity of inflowing water. Draw radius R\ at distance R\ on this radius draw a 114 HYDRAULICS AND HYDRAULIC MACHINERY. line inclined outward to R by angle o, whose tangent = 0.01 76iV12iV^Vi (i\r = r.p.m. Q = c\i. ft. per min. ri=ft. per sec). The vane curve must be tangential to this line. At the extremity of a radius draw a tangent and on this tangent, at a point distant I ('=;^s — r-^^ \ 2«i sin a/ as a center, strike an arc from the outer circumference of wheel to the inlet circumference, and this arc will be the vane curve. The case should start at zero cross-section and increase in one circum- ference to full discharge section by means of an Archimedean spiral. Hydraulic Bam. Water flowing in a pipe under a low head escapes through an opening at the end until it acquires a velocity sufl&cient to move a valve closing the outlet. This sudden stopping of flow creates an ex- cessive pressure in the pipe, and a valve near the end is opened which leads to an air-chamber into which the water rushes, and from there into a delivery-pipe. Equilibrium being restored the air-chamber valve closes, outlet valve opens and the cycle is repeated. Water may be raised 10 times as high as the head of the stream in ft. Efliciencjr, 50 to 75%. Pulsometer. In this device water is raised by suction into the pump chamber by a vacuum resulting from the condensation of steam within it ; it is then forced into the deh very pipe by the pressure of a fresh supply of steam. Two chambers are employed, one raising while the other dis- charges. Duty, 10,000,000 to 20,000,000 ft.-lbs. per 1,000 lbs. of steam. The Alr-Llft Pump, A vertical pipe with its lower end submerged in a well or tank is supplied with a smaller pipe from which compressed air enters into the bottom of the larger pipe. The column of liquid in the pipe, consisting to a certain extent of air- bubbles, is lighter than an equally high column of liquid not so aerated, and therefore rises. The efliciency ranges from 26 to 50%, where the ratio of submerged length to length above surface varies irom 0.5 to 2, respectively. As there are no moving parts, this device is valuable in the case of lifting acids, chemical solutions, sewage, etc. PLUNGER PUMPS AND PUMPING ENGINES. Quantity of Water Pumped. Q (in cu. ft. per min.) =0.00545Fd2; Qi (gals, per min.) =0.040766 Kd^, where F=speed of plunger in ft. per min. and <i = diam. of plunger in in. V ranges from 100 to 200 ft. per min., and in well-designed engines may reach 250 ft. if the waterways are ample and the water is not abruptly deflected. Loss by leakage and slip ranges from 5% for new, well-packed pumps to 40% for worn and badly cared-for apparatus H. P. Required to Raise Water a Giycn Height, H. (Theoretical.) H.P. - Q//-*- 529.2 = Q,// -5- 3,958.7, or, as 1 ft. // = 2.3 lb. pressure, p, H.P. = Op -J- 229.2 = Qip -i- 1 ,714.5. Theoretical lift for normal temperatures «=34 ft. When the temperature of the water increases, the pres.sure of the water vapor decreases the theoretical lift, which at 150** F. =*25.7 ft., at 175** F. = 18.5 ft., and at 200° F. = 7.2 ft. Hot water should therefore flow to the pump by gravity. Air-Cfaambers. Even flow and smooth running are obtained by the use of air-chambers, where the impact of the water is received and g^ven out as pressure. On the delivery side these should be from 3 to 6 times the caoacity of oump, and on the suction side from 2 to 3 times the capacity. High-Duty Pumping Engines. Small pumps are either driven from a crank-shaft or are direct-acting, i.e., having a steam cylinder in which the full pressure of the steam is used throughout the stroke. In large, high-duty engines the steam is used expansively. In the Worthington high-duty engines comnensating cylinders are em- ployed in order to equalize the driving force. These cylinders rock on trun- nions, are connected to an accumulator under a water pressure of about 200 lbs. per sq. in., and have their plungers pivoted to the, piump-rod. This arrangement ofl'ers a resistance to the steam pressure 'during the early part of the stroke, receiving energy during the period of full steam pressure and giving it out later when the pressure falls through expansion, thus maintaining a fairly ev^n efi'ective pressure throughout the stroke Duty. The old measure of numning-engine performance was the numbei of ft.-lbs. of work done per 100 lbs. of coal consumed. In 1S91 the A. S. M. E PLUNGER PUMPS AND PUMPING ENGINES 115 committee recommended that it be changed to the number of ft.-lbs. of work per million heat units furnished to the boiler ( = 100 lbs. coal where each lb. imparts 10,000 heat units, or where the evaporation from and at 212° F.=- 10.356 lbs. water per lb. of fuel). It is customary now to also state the duty in terms of the number of it.-lbs. of work per 1,000 lbs. of steam used. Performance of a Modem Pumping Plant. The following data are taken from a 24-hour duty .trial of one of the units of the Central Park Ave. pumping plant in Chicago (E. N., 5-26-04), and will serve as an illustra- tion of high-grade installations. Three Worthington high-duty, triple-expansion engines make up the plant, each with a rated capacity of 20,000,000 gals, per 24 hours against 150 ft. head. Cylinders are 21, 33, and 60 in. in diam., 50 in. stroke, steam-jacketed aU over. Superheated steam is used which is supplied by six 225 H.P. Scotch marine boilers, each with two 40 in. corrugated Morison fiunaces and 140 2^ in. tubes. Boilers are 10 ft. in diam. and 12 ft. long, fitted with Hawley down-draft furnaces. Steam pressure at throttle, h.p. and i.p. jackets and reheater coils, 114.45 lbs.; at I.p. jacket, 10.13 lbs. Vacuum in exhaust, near I.p. cyl. — 26.98 in. of mercury, barometer, 14.45 lbs. (The weights of pistons, plungers, etc., are exactly balanced by a water pressure of 78.97 lbs.) Delivery pressure of water = 52.23 lbs. = 120.65 ft. head. Height of delivery gauge above water = 32.24 ft. .*. Total head = 152.89 ft. Temp, of water -=72*» F., temp, of feed- water -102.18*' F., temp, of steam at throttle = 516.91° F. (superheated 154°) Total steam used in cylinders = 143,734 lbs. Steam used in jackets and reheater, 16,400 lbs. Total steam used, 160,134 lbs. Dry coal burnt to evaporate total steam, 18,534 lbs. R.p.m., 19.33. Piston speed, 159.74 ft. per min. Stroke, 49.587 in. Plunger displacement (24 hrs.), 22,086,318 gals. =2,952,400 cu. ft. = 183,934,538 lbs. Allowance for leakage and slip, 0.5%. Net work (24 hrs J, 27,981,142,800 ft.-lbs. Net delivered H.P =588.82. I.H.P. = 660.9. Efficiency. 89.15%. Steam per I.H.P. per hr.. 10.01 lb.; do., per net delivered H.P , 11.32 lb. Dry coal per I.H.P. per hr., 1.42 lb.; do., per net delivered H.P., 1.581b. Ck>mbu8tible per I.H.P. per hr., 1.07 lb.; do., per net delivered H.P., 1.2 lb. Duty: per 1,000 lbs. steam = 174,736,801 ft.-lbs. Duty per 100 lbs. coal — 150,971,958 ft.-lbs. Boilers Fuel, Maryland Smokeless coal. Upper grate surface, 35 sq. ft. Water heating surface, 1,402 sq. ft. Superheating surface: internal, 180 sq. ft., external, 375 sq. ft. Total coal burnt, 22,779 lbs. Per cent moisture, 0.88. Total dry coal, 22,519 lbs. Per cent ash and refuse, 8.17. Total water fed to boiler, 195,153 lbs. Factor of evaporation (including superheat), 1.166. Equivalent water evaporated into super- heated steam from and at 212°, 227,548 lbs. Dry coal per hour per sq. ft. of upper grate surface, 26.87 lbs. Equivalent evaporation from and at 212° per sq. ft. of heating surface, 6.7 lbs. Average steam pressure, 154.22 lbs. Temp, of feed-water entering purifier, 177.26° F. Temp, of escaping gases, 459° F. Degrees of superheat, 162. H.P. developed, 275. Actual water evaporated per lb. of coal fired, 8.567 lbs. Equivalent evaporation from and at 212° F.: of coal fired, 10.077 lbs.; of dry coal, 10.11 lbs.: of combustible, 10.97 lbs. Calorific value of dry coal per lb., 14,213 B.T.U.: do. of combustible, 15,634 B.T.U. Efficiency of boiler (based on combustible), 67.76%; do., including grate (based on dry coal), 64.52%. Cost of coal per ton of 2,000 lbs. , $2.89. Cost of coal to evaporate 1,000 lbs. water from and at 212° F., S0.151. A similar engine at 142.27 lbs. steam pressure, 71.2° superheat gave a duty of 157,133,000 ft.-lbs. per 1,000 lbs. steam used. The highest recorded duty (181,068,605 ft.-lbs. per 1,000 lbs. dry steam) is that of an AUis triple-expansion pumping engine at St. Louis, operating under 140 lbs. steam pressure. Another high-duty engine is a Reynolds triple-expansion vertical engine at Boston, 30,000,000 gals, capacity, operating at a piston speed of 195 ft. per min. under 185 lbs. steam pressure. Duty, 178,497,000 ft.-lbs. per 1,000 Iba. steam, or, 163.925,300 ft.-lbs. per million heat units. B.T.U. per I.H.P. per min. = 196. Steam per I.H.P. hour = 10.375 lbs. Coal per I.H.P. hour=1.06 lbs. Thermal efficiency, 21.63%, or, including economizer, 22.58%. 116 . HYDRAULICS AND HYDRAULIC MACHINERY. HTDftAULIC POWER TRANSMISSION. Water under high pressures (600 to 2,000 lbs. per sq. in.) is advantageously used where power distribution is desired over small areas, viz., wharves, boiler and bridge shops, for presses, cranes, riveting, flanging and forging machinery. The system consists of pumps to develop the desired pres- sure, from which the water flows through piping to an accumulator, which is a vertical cylinder provided with a heavily weighted plunger. Pipes lead from the accumulator to the machines to be operated. The work stored in an accumulator is eaual to the weight on plunger X height in ft. plunger is raised, or wH ft.-lbs. Accumulator efficiency may be 08%. Efficiency of a direct plunger or ram in a hydraulic crane is around 93%, decreasing in proportion to the number of multiplications of movement by pulleys. (Pressures used in boiler shops range from 1,500 to 1,700 lbs. per sq. in.) Effective pressure (lbs. per sq. in. ) = accumulator pressure (lbs. per sq. in.) X (0.84 —0.02 m), where m = ratio of multiplying power (H. Adams). Maximimi hoisting speeds in ft. per sec., warehouse cranes, 6; plat- form cranes, 4; passenger and wagon hoists, heavy loads, 2: plunger passenger elevators, direct stroke, 10. Cast iron should not be used for hydraulic cyUnders when pressures over 2,000 lbs. per sq. in. are used, W. I. pr steel being substituted. The test pressure should be about three times the working pressure. Desigrn of Hydraulic Cylinders. (Kleinhans.) Load on ram, in ton.«3 = 0.0003927pd2; thickness of walls of cylinder in in. =pZ )-^2(/-p); thickness of bottom end of cylinder- at center = O.bD'^p -^ / ; th ickness (at a radius D-^3) between center and wall diam. =0.433D'N/p-*-/; where p — water pressure in lbs. per sq. in. , d = diam. of ram or plunger, D — internal diam. of cylinder =d+l to 2 in., according to size, f—saie fiber stress = 10,000 for cast steel. The bottom of cylinder is spherical (of radius d) and rounded to wall of cylinder by a radius = 0.2d. Friction of Cup Leathers. F=»frictional resistance of a leather in lbs. per sq. in. of water pressure — 0.08p + (c-«-d), where d = diam. of plunger in in., p» water pressure in lbs. per sq. in., and c»100 for leathers in good condition, 250 if in bad condition. (Goodman.) SHOP DATA. THE FOUNDBT. Sand. Good, new sand contains from 93 to 95% of silica, 5% of alu- mina, and traces of magnesia and oxide of iron. Sand containing lime should not be used. Floor sand: old sand, 12* new sand. 4; coal duat. 1. Facing sand: old sand, 6; new sand, 4; coal dust, 1. (The numbers refer to parts by weight.) liOam is a mixture of clav, rock sand, powdered charcoal, cow hair, chaff, horse manure, etc. (for binding power and porosity) ground together in a mill. Cores require a mixture of rock ^nd and sea sand with a binding sub- stance, and are black-washed after baking with a mixture of powdered charcoal and clay water. Parting Sand. Powdered blast-furnace elax. brick dust or fine dust from castings may be used for this purpose. Plumbago, powdered char- coal, soapstone, and French chalk are used for facing moulds in order that smooth castings may be obtained. Consistency of Sand. If too much burnt, or old sand is used it wiU cake in the mould. Sand should be so moistened that if the hand is closed on a ball of same and then opened, the sand will just retain the shape given to it. Shrinkage of Castings. Patterns having one horizontal dimension under 3 in. should be made -it in. smaller to allow for rapping. Under ordinary conditions the shrinkage of castings per foot is as follows : cast and malleable iron, i in.; brass, aluminum, and steel, A in.; zinc, A in.: tin. ^ in. ; white metal, ^ in. ; gun-metal, ^ in. The edges of patterns should be rounded, all comers and ang^les being filleted in order to avoid the weakening due to crs^tallizatioD in coolina. TV^eights of Castings. Multiply weif^t of pattern by 12.5, 14.1, or 16.7, respectively, if the pattern is of red, yellow, or white pine and the casting is of iron. If the casting is of yellow brass, multiply similarly by 14.2. la or 19. To Clean and Brighten Brass Castings. In a glazed vessel mix 3 parts of sulphuric acid with 2 parts of nitric acid and add a handful table salt to each quart of the mixture. Dip the castings in the mixture and then thoroughly rinse in water. The Cupola. Speed of melting : W = 2d2V^. Air required • Q = 0.5d2V^. H.P. to operate fa,n=€p^n-*-3,800. In these formulas d = inside diam. of cupola lining in in., TF=»ibs. of iron per hour, p=air pressure at cupola in ounces per sq. in., and Q»cu. ft. of air per min. (E. N., 7-21-'04). THE BLACKSMITH SHOP. YTelding. Wroiight iron welds at a white, sparking heat (1,500** to 1,600** F.), sand being used as a flux and to prevent scale. Steel welds at lower heats, borax oeing the flux employed. Electric Welding. Extra sound welds can be made by abutting the surfaces of the parts to be welded, allowing an electric current of large volume to flow, and by forcing the parts together when the localized heat at the joint (due to the current) has attained the welding tempera-> ture. Alternating currents of low potential are used. In ^neral, from 25 to 30 H.P. applied to the generator are required per sg. in. of section to be welded. For iron and steel this power must be applied for [(area in 117 r 118 SHOP DATA. sq. in. X 18)+ 10] seconds. Copper requires 82 H.P. per sq. in. of section, and it munt be applied [(area in sq. in. X 17.5)+ 7] seconds. To Anneal Tool Steel, heat to an even red and cool slowly in a box, surrounding the steel by gravel and charcoal. Case-Hardening. Raise the pieces (W. I. or mild steel) to a red heat and apply equal parts of prussiate of potash and salt. Quench while the mixture is flowing, not waiting until it biu*ns ofl'. If extreme hardness is desired, use cyanide of potassium. (A dangerous poison.) Tempering of Steel. Harden by heating to a cherrjr red (1,660** F.), cooling quicfly in water, the article being kept in motion. To temper, brighten the surface of the article and heat slowly (not in contact with the flame) until the desired color (as below) appears, and then quench in water or oil. Very pale straw (430** F.), for brass scrapers, hammer faces, lathe and planer tools for steel and ivory, and bone-working tools. Light straw (450** F.), for drills, milling cutters, lathe and planer tools for iron. Medium straw (470** F.), for boring cutters. Very dark straw (490** F.), for taps, dies, leather-cutting tools. Brown-yellow (500** F.), for reamers, punches and dies, gouges, stone- cutting tools. Yellow-purple (520** F.), for flat drills for brass, twist drills, planes. light purpfe (530** F.), for augers, dental and surgical instruments. Dark purple (550® F.). for cold-chisels, axes. Dark blue (570** F.), tor springs, screw-drivers, circular saws for metal, wood-chisels, wood-saws, planer knives and moulding cutters. Forgings. Allowance for machining. Diam up to 5 in. 6 to 8 in. 9 to 10 in. 12 in. and larger Allowance 0.25 in. 0.375 in. 0. 5 in. 1 in. THE MACHINE SHOP. Punches and Dies. Diam. of hole in die = diam. of punch + (0. 16 to 0.3) X thickness of plate to be punched, according to various authorities A fair average value for the excess is 0.2 X thickness. Catting Speeds for Lathes, Planers, and Shapers in ft. per min. (Ordinary tool steel.) Amencan German. Practice. (Ing. Taschen- (J. Rose.) buch.) Hard cast steel 6 to 10 Tool steel _ 12 ^ 12 Machinery steel 15 to 20 18 to 30 Wrought iron 18 ' * 35 18 * ' 30 Cast iron 20'* 38 16 " 24 Bronze 60 " 120 40 " 90 Copper 150 " 350 40 " 90 Circumferential speed, ft. per min. = 0.2618 Xr.p.m.X diam. of piece in in. Planer speeds range from 18 to 22 ft. per mm. Maximum Feeds and Depth of Cuts (Ing. Taschenbuch): max, feed per rev. = 0.06 in. for roughing, and 0.2 in. for finishing; greatest depth of cut =0.4 in. for C. I., =0.28 in. for W I = 0.16 in. for steel, =0.12 in. for bronze. Max. planer feed per stroke = 08 to 0.16 in. for roughing, and 0.12 to 0.5 in. for finishing; greatest depth of planer cut = 0.8 in. for C. I., =0.5 in. for W. I., = 0.32 in. for steel, =0.16 in. for bronze. , v » , , , « Milling Cutters. (Ordinary tool-steel.) Angle of tooth: Front face radial- tooth angle, 50*'; angle at cutting edge = 85** (5% clearance V No. of teetn = 2.8 (diam. in in. + 2.6 in.). Take nearest even number. Speed, Depth Feed, ft. per of cut, in. per nun. in. mm. Hard steel 21 A Wrought iron 40 1 Mild steel 30 i Gun-metal 80 ♦ Cast-iron gears ^o t Hard cast iron oU Jt MACHINE SCREWS. 119 For light cuts, speed in ft. per min.: steel, 45; W. I., 60; C. I., 90; gun- metal, 105; brass. 120. For heavy cuts reduce these speeds about one-half. Twist Drills (of ordinary tool-steel). Revs, per min for iron: i in., 660; i in., 320; | in., 220; * in., 160; f in., 130; i in., 105; 1 in., 80; liin.. 54; 2 in., 39; 3 in., 26; 4 in., 17. For steel take 0.7 of these speeds, — for brass, multiply them by 1.25. Feed: — 125 revs, per inch depth of hole for drills under ^ in.; for larger drills allow 1 in. of feed per min. Morse Standard Tapers for Drill Shanks and Sockets. No. of taper. 1 2 3 4 5 6 Large Diam. A in. diam. of from hot- socket. tomof hole. 0.476 0.369 0.7 0.572 0.938 0.778 1.231 1.026 1.748 1.475 2.494 2.116 Depth of hole. C.toc. of slot drill- hole. Width of slot. 0.213 0.26 0.322 0.478 0.635 0.76 Diam. of tongue. 0.33 Length tongue. The tongues of drills are 0.01 in. less in thickness than the width of slot. Keys to force out drills are tapered i.75 in 12 (or 8® 19'). Taper Turaing. Distance tail-center is to be set over» total length of piece ^^ diflF. between diams. at ends of taper length of tapered part 2 As the centers enter the work an indefinite distance, this rule is only ap- proximate and the results must be corrected by trial. Machine Screws. Wire Threads Diam. driS. Wire Threads Diam. gauge. per in. in in. gauge. per in. in in. 2 56 0.0842 No. 49 12 24 0.2158 3 48 .0973 45 14 20 .2421 4 36 .1106 42 16 18 .2684 5 36 .1236 38 18 18 .2947 6 32 . 1368 35 20 16 .3210 7 32 .1500 30 22 16 .3474 8 32 .1631 29 24 16 .3737 9 30 .1763 27 26 16 .4000 10 24 . 1894 25 28 30 14 .4263 14 .4620 Tap drill. No. 17 13 6 1 i •* ^o. 2, i in. ; No. 4, f in. ; No. 6, 1 in. ; No. 8, U in. : 4, 2 in. ; No. 18, 2^ in. ; No. 22 and laroer, 3 in. ths up to i in., by 8ths from ^ to li^ in., and by 4thuB Maximum lengths: No. No. 10. 1* in.; No. 14, Lengths increase by 16ths i above l^ in. International Standard Threads (Metric). Angle of thread^eo**; flat i ht. of sharp V thread; root filled in ,V ht. Dimensions in mm. Diam. Pitch. Diam. Pitch Diam. Pitch. 6&7 1 18,20<*:22 2.5 48A52 5 8&9 1.25 24&27 3 56&60 6.5 lO&ll 1.5 30&33 3.5 64&68 6 12 1.75 36&39 4 72&76 6.5 14 A 16 2 42&45 4.6 80 7 Metric threads may be cut in lathes whose lead-screws are in inch pitch by introducing change gears of 50 and 127 teeth. (127 cm.=50 in., within 0.0001 in. For less accurate work a 63-tooth wheel will give an error of only 0.001 in. in 10 inches.) 120 SHOP DATA. Screw Threads. U. S. Standard. Whitworth. Diam. in in., d. Threads per in., n. Tap drills. U.S. Nuts — rough. Hex.— short diam. iquare- long diam. Threads per in.. Diam. at thd. bottom. % 2 2i l\ 3 3i it 4 w I* l\ 6 20 18 16 14 13 12 11 10 9 8 7 7 6 6 5* 5 5 4 4 3^ 3i 3t 3 3 « I i II s ^-: o2 • ■^■^ o . o3-^P .*^. 0) OS*. " 92 g^^-- 8S2+"5'5^3ii 0.7 20 18 16 14 12 12 11 10 9 8 7 7 6 6 5 6 4* 4* 4 4 3* 3i 0.186 .241 .295 .346 .393 .456 .508 .622 .733 .840 .942 1.067 1.161 1.286 1.369 1.494 1.590 1.715 1.930 2.180 2.384 2.634 Stubs' Steel Wl re Gaug e (con tinued from table on page 121 ). No. Diam. No. Diam. No. Diam. No. Diam. No. Diam. 41 0.095 52 0.063 72 0.024 F 0.257 P 0.323 42 .092 54 .055 74 .022 G .261 Q .332 43 .088 56 .045 76 .018 H .266 R .339 44 .085 58 .041 78 .015 I .272 S .348 45 .081 60 .039 80 .013 J .277 T .358 46 .079 62 .037 A .234 K .281 U . .368 47 .077 64 .035 B .238 L .290 V .377 48 .075 66 .032 C .242 M .295 W .386 49 .072 68 .03 D .246 N .302 X .397 60 .069 70 .027 E .25 O .316 Y Z .404 .413 WIRE AND SHEET-METAL GAUGES. 121 The U. S. Standard and Imperial flanges are respectively the le^ stand- ards in the tJ. S. and Great Britain. Stubs' steel wire gauge is used in measuring steel wire and drill rods. Wire and Sheet-lHetal Gauges. No. Ameri- Birming- ham — Stubs Wash- burn & Trenton U.S. Stand- ard. Impe- can « B.&S. Stubs (iron). (steel). Moen — Roebling Iron Co. rial. 0000000 0.49 0.5 0.5 000000 .46 .469 .464 00000 .43 .45 .438 .432 0000 0.460000 0.464 .393 .40 .406 .4 000 .409640 .425 .362 .36 .375 .372 00 .364800 .38 .331 .33 .344 .348 .324950 .34 .307 .305 .313 .324 1 .289300 .3 0.227 .283 .285 .281 .3 2 .257630 .284 .219 .263 .265 :266 .276 3 .229420 .259 .212 .244 .245 .25 .252 4 .204310 .238 .207 .225 .225 .234 .232 6 .181940 .22 .204 .207 .206 .219 .212 6 .162020 .203 .201 .192 .190 .203 .192 7 .144280 .18 .199 .177 .175 .188 .176 8 .128490 .166 .197 .162 .160 .172 .16 9 .114430 .148 .194 .148 .146 .156 .144 10 .101890 .134 .191 .135 .130 .141 .128 11 .090742 .12 .188 .12 .1175 .125 .116 12 .080808 .109 .185 .105 .105 .109 • .104 13 .071961 .095 .182 .092 .0925 .094 .092 14 .064084 .083 .180 .08 .08 .078 .08 16 .067068 .072 .178 .072 .07 .07 .072 16 .050820 .066 .175 .063 .061 .0625 .064 17 .046257 .058 .172 .054 .0525 .0563 .056 18 .040303 .049 .168 .047 .045 .05 .048 19 .035390 .042 .164 .0.41 .039 .0438 .04 20 .031961 .035 .161 .035 .034 .0375 .036 21 .028462 .032 .157 .032 .03 .0344 .032 22 .025347 .028 .155 .028 .027 .0313 .028 23 .T)22571 .025 .153 .025 .024 .0281 .024 24 .020100 .022 .151 .023 .0215 .025 .022 25 .017900 .020 .148 .02 .019 .0219 .02 26 .015940 .018 .146 .018 .018 .0188 .018 27 .014195 .016 .143 .017 .017 .0172 .016 28 .012641 .014 .139 .016 .016 .0156 .014 29 .011257 .013 .134 .016 .015 .0141 .013 30 .010025 .012 .127 .014 .014 .0125 .012 31 .008928 .010 .120 .0135 .013 .0109 .011 32 .007950 .009 .115 .013 .012 .0101 .0108 33 .007080 .008 .112 .011 .011 .0094 .01 34 .006304 .007 .110 .010 .01 .0086 .009 35 .005614 .005 .108 .0095 .009 .0078 .008 36 .005000 .004 .106 .009 .007 .007 37 .004453 .103 .0085 .0066 .0068 38 .003965 .101 .008 .0063 .006 39 .003531 .099 .0075 .005 40 .003145 .097 .007 .0048 Imperial Wire Gauge (continued from table). No 41 42 43 44 45 46 47 4S 49 50 Diam 0044 .004 .0036 .0032 .0028 .0024 .002 .0016 .0012 .001 Grinding Vnieels, The abrasives used in grinding wheels are corundum, emery (impure corundum), carborundum and alundum. The first two 122 SHOP DATA. occur in a natural state, while the latter are products of the electric furnace, are very much harder and have greater cutting power and durability. Carborundum (SiC) is composed of 30% Carbon+70% Silicon. Alundum is obtained principally from bauxite, an amorphous hydrate of alumina. Speeds. Peripheral speeds of wheels vary from 3,000 to 7,000 ft. per min., usually from 5,000 to 6,000. Cyhndrical work in grinding- machines should have a peripheral speed of from 25 to 80 ft. per min., the slower speeds for dehcate work. The traverse speed of wheel— face of wheel X 0.75 per rev. of piece being ground. Polishing wheels should have a peripheral speed of about 7,000 ft. per min. Grades of Wheels for Tarious Uses. Abrasives are classified (accord- ing to the sisse of their grains) by numbers which indicate the meshes per linear inch of the screen through which the crushed isubstance has passed. The cutting capacity of the various sizes compared with files is as follows: 16 to 30, rough files; 30 to 40, bastard; 46 to 60, second-cut; 70 to 80, smooth-cut; 90 and upwards, suoerfine to dead-smooth. The Norton Emery Wheel Co. gives the following table which is approxi- mately correct for ordinary conditions. (/>' medium soft wheel, M — medium, Q = medium hard; other letters indicate corresponding inter- mediate grades): No. of grain. Laige C. I. and steel castings (Q, A) 12 to 20 Large malleable and chilled iron castings (Q, A) 16 to 20 Small castings (C. I., steel and malleable iron), drop-forgings (,P,Q) 20 to 30 W. I., bronze castings, plow points (P, Q), brass castings (O, P) . . 16 to 30 Planer and paper-cutter knives (/, ^), lathe and planer tools (iV, O) 30 to 40 General machine work {.0*t*) 30 to 40 Wood-working tools, saws, twist-drills, hand-ground (il/, AT). ... 36 to 60 Machine grinding: twist drills (/C, Af), reamers, taps, milling cutters KH,K) 40 to 60 Hand grinding: reamers, taps, milling cutters (AT, P) 46 to 100 For grinding machines, the Lsndis Tool Co. gives the following: Material. No. of grain. Grade of wheel. Soft steel, ordinary shafts 24 to 60 Medium or one grade harder. • * • • tubing or light shafts.. . 24 ' * 60 One or two grades softer than medium. Hard steel and C. 1 24 " 60 Medium or one grade softer. Internal grinding 30**60 ** to seveiad grades softer. Economy In Finishing Cylindrical Work is obtained by reducing stock by means of rough, heavy cuts to within .01 to .025 in. of the finished diameter and then grinding to completion. It is possible to force wheels to remove 1 cu. in. per min. Emery Wheels vs. Filing and Chipping. The figures in the follow- ing table express approximately the number of lbs. removed per hour by the various processes. The metal bars ground were J in. Xi in., held against wheel by a pressure of about 100 lbs. per sq. in. (T. Dunkin Paret* Jour. Franklin Inst., 5-12-1904): B™«,. CI. W.I. Harde^ Emery wheel 34. 16.5 6. 6.87 FUe 1. .72 .34 .125 Cold chisel. ...-. 2.56 4.69 1.31 .187 Wheel wear .8 1.37 1.69 3.63 Grindstones for tool-dressing should have a peripheral speed between 600 and 900 ft. per min. Rapid grinding speeds should not exceed 2,800 ft oer min. High-Speed Tool Steel. In 1900 the Bethlehem Steel Co. exhibited tool steel at the Paris Exposition made and treated according to the Taylor- White patents. This steel was capable of taking heavy cuts at abnormally high cutting speeds, the chipH coming off at a red heat, and the tool stand- HIGH-SPEfiD TOOL STEEL. 123 ing up well under the work. Since that date many steels of similar capacity have been placed on the market by various makers. These steels are air-hardening an^l contain (in addition to carbon) one or more of the elements, chromium, tungsten, vanadium, molybdenum, and manganese, these elements uniting with the carbon to form carbides. Iron carbides exist generally in an unhardened state and at high tem- peratures these part with their carbon, which then shows a greater affinity for chromium, etc. These newly formed carbides may be fixed by rapid cooling, and they impart the extraordinary hardness which they possess to the steel. This hardness is retained by the steel, as these carbides are not affected by changes of temperature within certain limits. Tools made from these steels are forged at a bright red heat and slowlv cooled. The points are then reheated to a white, melting heat (about 2,000** F.). cooled to a red heat in an air-blast, and then slowly cooled, or quenchea in oil. Cutting Speeds for High-Speed Tool Steels. Experiments have been conducted in Germanv and also in England (by Dr. Nicholson of Manchester) to determine the best cutting speeds to employ on various metals, and the results are expressed by the following formula: Cutting speed in feet per minute, <S= — r—f + M, where a is the sectional area of cut in sq. in. (= depth X traverse in one rev.), and K^ L, M are con- stants: Whitworth Fluid (Manchester) Pressed Steel Soft. Medium. K - 1.95 1.85 L - 0.011 0.016 Af - 15 6 W.L 2.62 0.0002 23.5 Siemens-Martin Steel (Berlin). Soft. Medium. Hard. K - 4.03 0.918 1.17 L - 0.012 0.009 0.0076 M - -26 16 -20 Cast Iron. Cast Steel. 0.196 -0.0199 32.2 0.2 -0.005 11.25 The chemical composition of the metals experimented upon is as follows: CAST raoN. Berlin. Carbon, combined 0.46 Graphite 3. 46 Si 2.05 Mn 1 S 0.1 P 0.1 Crushing strength in tons of 2,240 lbs. Manchester.- Carbon 0.3 0.54 Si 0.05 .21 Mn 58 .93 S 05 .025 P 07 .05 Tensile strength in tons (2,240 lbs.) . 26 to 32 40 STEEL. Siemens-Martin . Soft. Medium. Hard. 0.63 .20 1.22 .05 .05 49 Soft. 0.198 .055 .605 .026 .035 26 Whitworth. Medium. Hard, 0.275 .086 .65 .037 .043 29 0.614 .111 .792 .033 .037 47 Shop Practice. The following data have been reported in the technical joumaui of the past year, and may be taken as an index of good average Iffactice, when aurability is considered as well as a higJi cutting rate. 124 SHOP DATA. TURNING. Material. Speed, ft. Area of cut in Tool steeL permin. sq. in. MUd steel 140-160 0.0117 toO. 035 A.W. 0.5 carbon steel. 40-70 .0234** .0468 Cast iron. 40-70 .0078** .0936 " ** *• rolls (hard). .... 60 .0117" .039 Gun-metal 60 .02 '* .063 Chrome and high-carbon steels 17 .0125'* .02 0.4 carbon steel and C. I.. . 240 .01 ** .032 Various Am. steels. Tough alloy-steel shells. .. . 45-90 .0019'* .0273 Blue chip. PLANING. C. I. and mild steel 30-36 0.0117 to 0. 18 A. W. BORING. 0.5 carbon steel 60 3^ hole, ^ in. feed. A. W. C. I. . 40-50 .0125 too. 19 DRILUNG. Si«.. R.p.m. F^f r C.I lin. 360 6 in. A.W. C. I. and mUd steel 1 ** 250 5** '• '• ** ** H" 275 3.6in. " Hard steel 2 ** 80 0.83" C.I 1 •* 300 3.5** /CampbeU. Laird MQd steel 1 " 300 2.25" \& Co., "0172" C. I. and soft steel lA in. 260 3.25" (W.R.McKeen) 4 C. I. * * ^MAchinery Steel. . c:--> n-'ii !?»>»« Feed, in. -r „ m Feed, in. SizeDnll. R.p.m p©r iiin. R.P.m. permin. iin 390 10 320 3 1 ** 260 12 260 4 li ** 225 6 220 2 (Rand Drill Co.'s experiments, Am. Mach., 2-16-05.) Turning: — Cincinnati Milling Machine Co.'s practice. Roughing. / Speeds in ft. per min. » Area of cut. C. I. Steel. Facing C. I. .0005 80. in. 200 .001 *^ •* 130 125 125 .0015 ** *• 100 94 90 .0025 ** ** 66 66 64 .004 *• ** 62 62 60 .008 " " 60 68 40 Finishing. . 00005 sq. in. 300 .000125 *'^ ** 250 200 300 .00025 " " 200 150 188 .0005 ** ** 143 125 125 .001 •* ** 97 100 60 .002 *' ** 58 72 (T. A Sperry, Am. Mach., 5-25-05.) Steels: "A. W." (Armstrong- Whit worth) results are from reports of J. M. Gledhill, "Blue Chip" steel is made by the Firth-Stirling Steel Co.: ".0172" steel is maie by Campbell, Laird & Co., Sheffield: Drill data credited to W. R. McKeen are from a paper on Ry, Shop Practice, re- printed in Ry. Gazette, 7-8-04. Pressures on Cutting Tools, p, in lbs. per sq. in. Cast Iron: soft, 115,000; medium, 188,000; hard, 184,000. Steel: soft, 258,000; medium, 242,000; hard, 336,000. HIGH-SPEED TOOL STEEL. 125 ^ MILUNQ. > Material. Cutter. Speed. ^^^^ pe^SS^ TooU C. 1 4 in. 90 ft. 2X A 27 in. Blue Chip. •• 3*' 40** 8Xi 10.7** ** ** • 4 •• 82** 2xi 10 *• •*.0172" Steel 4" 103** 2Xi 6 ** C.I 9in.(face) 80 *• 6Xi 8.5** A. W. MUd steel 2f in. 72" 3XA 7.6** C.I 2i " 87" 2fxi 26 ** Steel gears (0.34 to 0.6 carbon) 8 " 67 " i deep 3.6 ** " Metal Removed in Unit Time. Cast Iron: lbs. per inin. = 3.13 Sa; lbs. per hour =187.8 Sa, Steel: lbs. per min. = 3.4 <Sa: lbs. per hour = 204 Sa. Power Required by Cutting Tools (lathes, planers, shapers, boring mills). H.P.=»paiS -5- 33,000. For milling machines J. J. Flather states that H.F. = cw, where ti; = lb8. removed per hour, and c»=0.1 for bronze, 0.14 for C. I. and 0.3 for steel. Best Tool Angles. Dr. Nicholson indicates in his dynamometric experiments that the tool edge (in plan) should be at an angle of 46° to the center line of the work, the clearance from 6 to 6°, the tool angle about 65° for medium steel (75° for C.I.) and the top-rake 20° for medium steel (9° for C.I.). (A. S. M. E., Chicago, 1904.) Average cutting stress: C.I., 160,000 lbs. per sq. in.; steel, 180,000 lbs. H.P. = cutting stress X a X -S -i- 33 ,000. Cutting H.P. for 1 lb. per min. = 1.46 for C.I. and 1.6 for steel. H.P. lost in tool friction =0.3 H.P. per lb. per min. /. Gross H.P. « 1.76 for C.I. and 1.9 for steel. The surfacing force for best shop 'angle (70° for steel) = 67,000 lbs. per sq. in. of cut; similarly, traversing force = 20 ,0(X) lbs. per sq. in. The surfacing force will thrust the saddle against the bed if the coefScient of friction equals or exceeds 0.333. The total net force to be overcome by the driving mechanism of the carriage for cutting steel = (67,000 XO. 333) + 20.000=42,333 lbs. per sq. in. of cut. Round.-nose tools are preferably used. High-Speed Twist Drills. Power required oc r.p.m.; thrust oc feed per rev. Thrust increases more rapidljf than the power consumed, consequently less power is required to drill a given hole in a given time by increasing the feed than by increasing the r.p.m. The angle of drill-point may be decreased to as low as 90° (standard angle = 118°), thereby reducing the thrust 26% and without affecting the durabihty of point. (W. W. Bird & II. P. Fairfield. A.S.M.E.. Dec, 1904.) Metal -Cutting Circular Saws. Cutting cold metal: diam., 32 in.; thickness, 0.32 in.; width of teeth ^cutting edge), 0.44 in.; teeth 0.2 to 0.6 in. apart; circumferential velocity, 44 ft. per min.; feed, 0.006 to 0.01 in. per sec. Cutting metal at red heat: diam., 32 to 40 in.; thickness, 0.12 to 0.16 in.; teeth 0.8 to 1.6 in. apart; depth of teeth, 0.4 to 0.8 in.; circumf. vel., 12;000 to 20,000 ft. per min. (Ing. Taschenbuch). Taylor- Newbold Saw, with inserted teeth of high-speed steel: A 9i in. cold saw at 76 r.p.m. will cut through 1} in. hex. cold-roUed steel in 26 seconds, and at 96 r.p.m., in 22 sees. A 36 in. saw, ^ in. thick, teeth averaging A in. thick, running at a cutting speed of 86 ft. per min. will cut off a bar of 0.36 carbon steel 14 in. X8f in. in 20 min. A bar of 0.40 carbon steel 6X5i can be cut in 4.4 min. Fits (Running, Force, Driving, Shrink, etc.). In the following table, which is derived from good practice, the first column ^ves the nominal diameter of hole. The mean value for each class of fit is given and also the permissible variation above or below same. For force, shrink, and driving fits the values given are those by which the diameter of the piece should exceed that of the hole, while for running and push fits they are the values by which the diameter of th& hole should exceed that of the piece. Force and shrink fits are given the same value. Push fits are those in which the piece is forced to place by hand-pressure. Running fits are given three values: A, for easy fits on heavy machinery; B, for average nii^-speed shop practice; C» for fine tool work. 126 SHOP DATA. Force + Drive + Push- Running— Diam. A. B. C. in in. Mean Var. Mean Var. Mean Var. Mean Var. Mean Var. Mean Var. 0.5 .75 .25 .37 .12 .5 .12 1.5 .5 1 .25 .6 .12 1 1.75 .25 .87 .12 .75 .25 2 .75 1.5 .5 1 .25 2 3.5 .5 1.25 .25 1.25 .25 2.6 .87 1.9 .62 1.15 .4 3 5.25 .75 2 .5 1.75 .25 3.1 1.1 2.3 .8 1.5 .5 4 7 1 2.5 5 1.75 .25 3.8 1.2 2.7 .85 1.6 .6 5 9 1 3 .5 2.25 .25 4.4 1.4 3.1 .9 1.87 .62 6 11 1 3.5 .5 2.25 .25 5 1.5 3.5 1 2 .75 The values above given are in thousandths of an inch ; thus, for a driving fit in a hole of 4 in. diam.. the piece should be 4.0025 in. in diam. (It may be either 4.002 in. or 4.003 in. and still be within the permissible vanation of 0.0005 in. either way.) For locomotive tires and other large shrunk work. Allowance in thousandths of an inch«(HX diaM. in in.)+ 0.5. (S. H. koore, A.S.M.E., 1903.) Sizes above 6 in. Diam. t For shrink fits add 0.0025 in. to diam. of piece for each inch ok diam. of hole where the part containing the hole is thick and unyielding. Where the metal around the hole is thin and elastic, add 0.0035 in. per in. of diam. For force fits multiply diam. of hole by 1.0007 and add 0.004 in.; variation of 0.001 in. is permissible. For drive fits allow one-half of the excess just given for force fits. For running fits, multiply diam. of hole by 0.000125; add 0.00225 in. and subtract this sum from diam. of hole, thus giving diam. of piece. Variation of 0.001 in. permissible. Power Required by Machinery. Machine. Material. No. of tools. H.P. working. H.P. light. Wheel Uthe. 84 in C. I. Boring mills, 54 to 78 in. . . C. I. Slotting machines, 36X12 and 40X15 W. I. Planers: Sellers, 62 in. X36 ft W. I. 36 in. X 12 ft •• 56in.X24ft Radial driU, 42 in Shaper, 19 in. stroke ' * (Baldwin Loco. Works; measurements by se(>arate electric motors.) 2 1 6 4.5to6.5 1.5 2.5 1 6.3<k7.3 1.5 A 2 2 2 2 in. drill 1 24.5 12.5 16.8 2.1 7.3 5.8 3 6 1.1 1.8 Machine. H.P. of motor required to operate under best conditions. Niles planer, 10 ft. X 10 ft. X 20 ft. Pond •* 8 •• X 8 •* X20 " •• 5i'* X 5" X12'* Gray *• 28 in. X32 in X6 ft. , iv GisEolt turret lathe, 28 in. swing W. F. and J. Barnes drill press, 21 in . 25 15 3 4 ^ 1 Niles radial drill, 60 in. arm 2 Emery Grinder, two 18-in. wheels in use, 950 r.p.m. ... 5 Pond Vertical Boring Mill, 10-ft. table 12 Bement & Miles Blotter 7 Jones & Lamson Turret Lathe, 2 in. X 24 in 1.5 Gisholt Tool Grinder 4 Hendey-Norton Lathe, 16 in 2 Putnam Lathe, 18 in 2.1 Pond •* 36 in 10 (F B. Duncan, Engineers' Society of W. Pa.) COST OF P^jWER and POWER PLANTS. 127 Motor H.P. Punch and Shears, li-in. hole in 1-in. plate, 6 H.P.) -.^ shearing 1-in. plate, 16 H.P. J ^^ Plate-edge Planer, 35 ft. X 1 in. 30 15ft.Xf in 25 Wood Planers 4-16 Circular Saws 4-24 (D. Selby Bigge.) H. P. of Motors for Machine Tools. Ordinary lathes: H.P.» 0.155—1; Heavy lathes and boring mills under 30 in.: H.P. =0.2345- 2; Boring niills over 30 in. swing: H.P. =0.255—4; Ordinary drill presses: H.P. = 0.065; Heavy radial drills: H.P.«0.15; MUling machines : H.P.= 0.31^ Planers (2 tools), ordinary: H.P.=0.25Tr; Do., heavy; H.P.= 0.41 Ty (Ratio of planer feed to return = l:3). Slotters: 10 in. stroke, H.P. = 6: 30 in. stroke. H.P. = 10; Shapers: 16-in. stroke. H.P. =3; 30 in. stroke, H.P. = 6.5. In the above 5 = swing in inches and IT » width between housings in inches. Formulas based on the cutting by ordinary water-hardened steel tools at 20 ft. per min. (J. M. Barr, in Electric Club Joumul.) If high-speed steels are used, the power required will be from 2.6 to 3 times tne above figures on account of increased speeds and cuts. Power Absorbed by Shaftinfc* In cotton and print mills about 25% of the total transmission ; in shops using heavy machinery, from 40 to 60%. Ii^ average machine-shops 1 H.P. is required for every three men employed. COST OF POWER AND POWER PLAKTS. Water Power. Cost of plant per H.P., including dam, $60.00 to $100.00; without dam, $40.00 to $60.00. Power costs from $10.00 to $15.00 per year per H.P. Steam Power. Cost of engines per H.P.: Simple, slide-valve, $7.00 to $10.00; simple Corliss, $11.00 to $13.00; compound, slide-valve, $12.00 to $16.00; compound CorUss, $18.00 to $23.00; high-speed automatic, $10.00 to $13.00; low-speed automatic, $15.00 to $17.00. Plain tubular boilers, per H.P., $10.00 to $12.00; water-tube boUers per H.P.. $15.00. Pumps, $2.00 per H.P. for non-condensing, and $4.00 for condensing. (Dr. Louis Bell in **The Electrical Transmission of Power.") Total cost of plant ranges from $50.00 to $75.00 per H.P., exclusive of buildings. Dynamos and other electrical apparatus, including switch-boards, cost from $20.00 to $36.00 per kilowatt capacity ($15.00 to $26.00 per H.P.), making the cost of an electrical power plant range from $65.00 to $100.00 per H.P. The cost of a H.P. hour has been estimated by various authorities to range from 0.55 to 0.85 cents. Dr. Bell places it at 0.8 to 1.00 cent with larj^, compound-condensing engines, and at 1.5 to 2.5 cents with simple engines, basing his calculations on a day of 10 hours, under full load. If the load is fractional and irregular, these figures should be altered to 1.00 to 1.5 cents and to 3 and 4 cents, respectively. The cost of electric power includes the cost of steam power to operate the generators, interest, repairs and depreciation on the apparatus, attend- ance, etc. In very large power plants under good load conditions the cost per kilowatt hour (1.34 H.P. hour) may be as low as one cent, at the bus oars. Gas Power. The cost of plant is about the same as that of a steam Slant. The gas consumption per brake H.P. per hour is about as follows: Tatural gas, 10 to 12 cu. ft.; coal gas, 16 to 22 cu. ft.; producer gas, 90 cu. ft.; blast-fur.ia(0 »ras, 116 cu. ft Coal consumption when producer gas is used is about 1.25 lbs. per B.H.P. With dollar gas, 1 B.H.P. costs 2 cts. per hour. One B.H.P. in a gasoline engine costs about 1.5 cents per hour, in an oil-engine about 1.75 cts. per hour, and in a Diesel engine from 1 to 2 cents, according to the cost of oil in the locality. 128 SHOP DATA. Proportions of Parts in a Series of Machines. When two siaes of a machine have been constructed and it is desired to extend the series or to introduce intermediate sizes, the following method of Dr. Ck>leman Sellers may be employed ^ Let D be the larger nominal dimension, say 30 (of a 30-in. swing lathe) •• Di " " smaUer " " '^ 12 ( " 12-in. " " ) Let diam. of lead-screw on D = C=3 in., and diam. of lead-screw on Di=ei = 1.5in. Thn D-D, = 30 -12 = 18, and C-Ct -3- 1.5. = 1.5. (C- Ci)-^(Z>-i>,) = 1.5-4- 18=0.0833=^, a factor. ^i>i -0.0833X12=1. Ci—^Di=» 1.5 — 1=0.5 = /, the increment. Let it be desired to find C2 when D2 = 20 in. Then C2 = (D2XA)-|-/=(20X0.0833)+0.5 = 2.16in. Hoisting Engines. Theoretical H.P. required = weight in lbs. (of cage, rope, and load) X speed in ft. per min. 4-33,000. Add 25 to 50% for actual H.P. on account of friction and contingencies. Max. limit of rope length in ft. a; = = , where / is the breaking strength of rope in lbs. per sq. in., to = lbs. per foot of rope, D=dead weight to be lifted, in lbs., and 7= factor of safety. Elevators. Speeds: low, to 150 ft. per min.; medium, 150 to 350 ft.; high, 350 to 800 ft. Counterweights should be about 75% of the weigkt of car and plunger. Floor area, 20 to 40 S9. ft. Number of elevators for a high office building = (Height of building in ft.X330)-Kspecd in ft. per min. X interval between elevators in seconds). (G. W. Nistle, A. S. M. E., May, '04.) Wire ropes for elevators (6 strands, each of 19 wires): Safe working load in lbs. = 1 1 ,600c?2 - 720,000^ (for Swedish iron) ; = 23,200rf2 - 760.000^ (for cast steel), where <f =»diam. of rope in in. and D**diam. of sheave in in. (Capt. H. C. Newcomer U. S. A., E. N., 1-15-03.) Conveyor Belts. Lbs. conveyed per min. «fe%>F-i- 13,824; lbs. per hour =62u,F-i- 230.4; tons per hour = 62«?r-i- 460,800, where 6=width of belt in in., F=s(>eed in ft. per min., w=lb8. in 1 cu. ft. of the substance conveyed. These values are for flat belts ; for trough belts multiply by 3. Average F=»300; higher speeds may be used, up to 450 for level and 650 when elevating at an angle. Approx. H.P. required to operate — lbs. per min. X elevation in ft. -«- 16,500. Electric Cranes. An electric travelling crane consists of a bridge, or girder, a trolley running on the bridge and a hoist attached to the trolley, each part being operated by its own motor. The following data are from a paper by S. S. Wales, read before the Engineers' Societv of W. Pa. Z/ = working load on crane, in tons; Tr = weight of bridge, in tons; «; = weight of trolley, in tons; jS» speed in feet per min.; P and Pi=» tractive force in lbs. per ton. , Bridge. s " / ^Trolley. -s Span. W. P. L. w. Pi. 25 ft. 0. 3L 30 lbs. 1 to 25 tons 0. ZL 30 lbs. 50 •* .6L 35 " 25 '• 75 " .4L 35 ** 75 " l.OL 40 '* 75 " 150 *' .bL 40 ** 100 '* 1.5L 45 •* H.P for bridge = P'S(L-l-TF-l-u?)-4-33,000. (Use motor 1.5 times as large.) HP for trolley =P,iS(L-l-w;)-j-33,000 ( " " 1.25 " ** ** ) H.P. for hoist =Z/fi:-*-10( = l H.P. per ton lifted 10 ft. in one minute). Speeds in Feet per Minute (Ing. Taschenbuch). 5 tons. 25 tons. 50 tons. 100 tons. Hoist 14 to 28 10 to 12 6 to 7. 5 5 Bridge 180 •* 300 140 " 210 130 *' 200 120 TroUey 80 " 120 50" 75 35*' 55 25to35 MISCELLANEOUS. 129 Paint and Painting* One gallon of linseed oil plus 40 lbs. of white lead will cover 250 to 350 sq. ft. of outside work with a good first coat. The same quantity will second-coat and finish from 350 to 450 sq. ft. White lead when used on inside work turns blaokish-A^Uow on account of exposure to the sulphur- ous fumes from gas or coal. White zinc is accordingly preferable for inside work, but, having less opacity, more coats are requirea. For iron- and steel- work red lead (40 lbs. per gal. of oil) is an expensive but durable covering. To prevent blistering on outside work boiled oil should be used. Turpentine only should be used for thinning. Knots and pitchy surfaces on wood should be coated with shellac varnish, and all grease, scale, acid, and moisture should be removed from metal work before painting. Graphite mixed with linseed oil and laid on in fairly thick coats makes a good paint for metals. Iron pipes, stacks, boiler fronts, etc., are varnished witn asphaltum thinned with turpentine. ELECTROTECHNICS. ELECTRIC CURRENTS. Resistance (svmbol R) is that property of a material which opposes the flow of an electric current through it. The unit of measurement is the ohm, which is a resistance equal to that of a column of pure mercury at 0® C, of uniform cross-section, 106.3 centimeters in length and weighing 14.4521 grams. Electro-motive Force (s3anbol E, abbreviation E.M.F.) is the electric pressure which forces a current through a resistance. The unit of meas urement is the volt, the value of which is derived from the standard Clark oeU whose E.M.F. at 16° C. is 1.434 volts. Current (/). An E.M.F. applied to a resistance will cause a flow of electricity which is termed a current. The \mit of measurement is the ampere, or the current which flows through a resistance of one ohm when it is subjected to an E.M . F. of one volt. One ampere is the amount of current required to electrolytically deposit 0.001118 gram of silver in one second. Quantity (Q). The quantity of electricity passing through a given cross-section oi conduct yr i i measured in coulombs. One coulomb is the quantity of electricity which flows past a given cross-section of a con- ductor in one second, there being a current of one ampere in the conductor. Capacity (C) is that proT)erty of a material by virtue of which it is able to receive and store up (as a condenser) a certain charae of electricity. A condenser of unit ca acity is one that will be charged to a potential of one volt by a quantity of one coulomb. The unit of capacity is the farad, which is too large for convenient use, — the microfarad (one millionth of one farad) being employed in practice. Electric Energy (W), or the work performed in a circuit through which a current ^ws, is measured by a unit called the joule. One joule is equal to the work done by the flow of one ampere through one ohm for one second. , Electric Power (P) is measured m watts. One watt is equal to the work done at the rate of one joule per second. One H.P.-746 watts. One watt = 0.7373 ft.-lbs. per sec, =0.0009477 B.T.U. per sec. One kilowatt =1,000 watts = 1.3405 H.P. Subdivisions and Multiples of Units are expressed bv the use of the following prefixes. One-millionth, micro; one-thousandth, milli; one million, meg-a, one thousand, kilo (e.g., microhms, microfarads, milli- amperes, megohms, mega volts, kilowatts, etc.). Aids to a Conception of Electrical Magnitudes. One ohm^resist- ance of 1,600 ft. of No. 8 copper wire (i in. diam.) approx., = resistance of 400 ft. of No. 14 copper wire (A in. diam.) approx. One volt =90% of the E.M.F. of a Daniell cell (Zn, Cu, and a solution of copper sulphate), 66% of the E.M.F. of a Leclanche cell (carbon-zinc telephone battery), approx. A 2,090 candle-power (c-p ) direct current arc lamp has a current of about 10 amperes flowing through it, and an E.M.F. between the carbons oi about 45 volts; it consequently requires 450 watts of electric power. 130 ELECTRIC CURRENTS. 131 An ordinary 16 c.-p. incandescent lamp on a 110-volt circuit requires about 0.5 ampere, its resistance being about 220 ohms and its power consumption about 55 watts. Ohm's Law. If .B is the difference of potential (E.M.F.) in volts between two points in a conductor through which a steady, direct current of / amperes is flowing, and the resistance of the conductor between the two points is B ohms, then ^— tt. or E=IR. Divided Circuits. If a current arrives at a point where several paths are open to its flow, it divides itself inversely as the resistances of these paths, or directly as their respective conductances. (The conductance of a circuit is the reciprocal of its resistance, or -=•• ) ti : t2 : ts""— •' — : — » IC ^ ri r2 ra etc., and 11+12+13 = *. The total conductance of the branched circuits, -s-— — I 1 — , etc., and R n r2 ra the reciprocal of this value equals the joint resistance of the several paths. For two branches -g-^ — I — , and /2= — 7-^. U ri r2 »'i + r2 KIrchoff's Laws. 1. The sum of the products of the currents and resistances in all the branches forming a closed circuit equals the sum of all the electrical i^ressures in the same circuit, or IE=I{IR). 2. At every ^oint in a circuit, II ~0^ or the sum of the currents flowing toward the joint equals the sum of the currents flowing away therefrom. Besistance of Conductors. The resistance R (in ohms) of a con- ductor of length I (in cms.) and cross-section 8 (in sq. cms.) is R — d-i-a^ where c is the specific resistance of the material (the resistance between two opposite faces of a cube 1 cm. long and 1 sq. cm. cross-section). Specific Resistances at 0® C. are given in the following table. When any higher temperature is taken, add as a correction 6Xdegs. C. above 00. Specific re- 6. sistance in &. microhms. 0. 004 Nickel 12. 323 0. 00622 .00428 Tin 13.048 .0044 . 00327 Lead 20. 38 . 00411 . 00435 Mercury 94. 07 . 00072 . 00406 German silver. . . 29 . 982 . 000273 . 00625 Carbon 4.200 to -0. 2 . 003669 i 40,000 Specific re- sistance in microhms. SUver 1.468 Copper. 1.561 Gold/. 2. 197 Aluminum 2. 665 Zinc 5.751 Iron 9.065 Platinum 10.917 Dilute Sulphuric Acid. Per cent wt. of H2SO4 in solution . . 5 15 30 45 60 80 Sp. res. at 18** C. in ohms 4.8 1.9 1.4 1.7 2.7 9.9 (For each deg. C. rise in temp, subtract 1.4% from above values.) Joule's Law. If a current of / amperes flows through a resistance of R ohms for t seconds, the heat developed, = PRt, in joules or watt-seconds» = 0.239 /*/2« gram-calories, = 0.0009477 Pfi^ B.T.U. The heat developed is equivalent to the energy causing the current flow. Rate of expenditure of energy, in watts, = J^/=/2JB. Energy in joules or watt-seconds = JS?/^=/2fi<. Electrolysis is the separation of a chemical compound into its con- stituent elements by means of an electric current. Two plates or poles (electrodes) are inserted in the compound or electrolyte, the electrode of higher potential being called the anode, and the other the cathode. The Sroducts of the decomposition are called ions. A current / amperes owing thr9ugh an electrolytic bath will deposit a weight of G grams in t units of time. G^kalt, where a is the chemical equivalent of the substance. If f is in seconds, A;=0.000010386; if « is in minutes, A;=0.0006232, and if t is in hours, A— 0.03739. The electro-chemical equivalent = grams per coulomb. 132 ELECTROTECHNICS. Grams Grams per per **• coulomb, amp. hour. a. Grams Grams per per coulomb, amp. hour. Aluminum 9 0. 00009347 0. 3365 Copper 31.6 . 00032820 1 . 1815 Gold. 65.4 .00067924 2.4453 Lead 103 . 2 . .00107 184 3 . 8585 Mercury. . . 99.9 . 00103756 3.7352 Nickel. . . . 29.3 .00030431 1.0955 Nitrogen.. 4.6 .00004840 0.1742 Oxygen. . . 8 Platinum. .97.2 Potassium. 39 Silver 107.7 Tin 58.7 Zinc 32. 4 0.00008309 0.2991 .00100952 3.6343 .00040506 1.4582 .00111867 4.0269 . 00060966 2. 1948 .000336611.2114 (To obtain pounds per ampeFe-hour, multiply grams per ampere-hour by 0.0022046.) a^ •o^ ELECTBO-MAGXETISM. Lines of Force. When a current starts to flow in a conductor* whirls of magnetism are generated around the conductor which seem to spring from its center, and the region so filled with these whirls increases radially in extent as the current increases, remains constant when a steady current is attained, and snrinks radially to nil when the current is interrupted. If the conductor is bent into a loop, an elementary electro-magnet is ^ j^ ^ formed, with a pole on either side of the "^ plane of the loop. If the conductor be wound into a number of loops along the surface of a cylinder, a solenoid is formed and the whirls so add themselves together that they may be considered as loops, entering the solenoid at all points of tiie section at one end, passing along inside parallel to the axis of the solenoid to the other end, thence emerging and returning _-. _^ outside in curved paths to the point Fl£.27. first considered (Fig. 27). These loops are termed lines of force, and their number depends on the number of spirals of conductor in the solenoid and the number of amperes of current flowing through them, or, as it is expressed, by the number of ampere-turns. The Intensity of the Magnetic Field (3C) at any point is measured by the force it exerts on a unit magnetic pole, the unit intensity, there- fore, being that which acts with a force of one dyne upon a unit pole, or one line of force per sq. cm. (A dyne is the force which, acting for one second upon a mass of one gram, imparts a velocity of one centi* meter per second.) Masneto-motive Force (^) is the magnetizing force of an electric current flowing in a coil or solenoid and is usually stated in ampere-turns. ff = 47m/-4-10 = 1.257n/, where n is the number of turns or loops of the conductor and / the current in amperes. The unit for ^ is called the gilbert and is equal to 0.7958 ampere-turns. ' " ' ■" .ce oer umt ienflrtli c » length in -. . - ^ .9SnI-hLi. '('Magnetic Induction ((B) is the magnetic flux or the number of lines of force per unit area of cross-section, the area at every point being normal to the direction of the flux. ® = /tSC, where /i is the permeability. The unit is the gauss, or one maxwell per normal sq. cm. The Magnetic Flux (*) is equal to the average field intensity X area. The unit is the maxwell, or the flux due to unit magneto-motive force (M.M.F.) when the reluctance is one oersted. Reluctance ((R) is the resistance offered to the magnetic flux by the material undergoing magnetization. The unit is the oersted, or the re- sistance offered by one cubic centimeter of vacuum. Magnetic Susceptibility, (ic)=JF-5-aC. ♦ B, F, and H are commonly used in place of (B, SF, and 3C. The Intensity of the Magnetizing Force per unit length of solenoid (5C)==4 ?m/-t-Z/ = 1.257 n/ -i-L, where 17= length in cm. If Li= length in inches. 5C = 0.495n/-^Za or, if expressed in lines per sg. in., 3Ci =3.193n/-*-Z^. ELECTRO-MAGNETISM. 133 Beluctlyity (v) is the reluctance per miit of length and unit cross* section. =1 -*-/«. Maxwells = gilberts -4- oersteds. Hysteresis. When a magnetic substance (e.g., iron) is magnetized, the intensity of magnetization does not increase as rapidly as does the magnetizing force, but lags behind it. This tendency is termed hysteresis, and it may be considered as an internal magnetic friction of the molecules of the substance. Continued rapid magnetizing and demagnetizing will cause the substance to become heated. Hysteresis (A) may be calcu- lated by the following formula due to Steinmetz : h (in watts) = nffli-^ArnlO""^, where A; = volume in cu. cms. and n = number of complete cycles of mag- netisation and demagnetization per second. 1?. Very thin, soft sheet iron. ... 0. 0015 * ' soft iron wire 002 Thin sheet iron (good) 003 Thick " " 0033 Ordinary sheet iron 004 Soft, annealed cast steel 0. 008 * * ma6hine steel 0094 Cast steel 012 Cast iron 016 Hardened cast steel 025 The Magnetic Circuit. Magnetism may be considered as flowing in a magnetic circuit in the same manner as an electric current does in a conductor and the following relation holds: ,_ -• xn Magneto-motive Force ,• u • i j. n Magnetic Flux = ^-j — , which is analogous to Cur- E.M.F. Reluctance Resistance* #«*iF-«-(R. Reluctance, (Jl=i-i-/:ta, where Z= length of magnetic circuit, a = area of cross-section and « = permeability (see Dynamos). *=JF-«-Ol, ^l I JF = 1.257nJ; .'. nl=' =-;;=;= =0.7958* — , where I is in cms. and a in /ta-i- 1.257 pa sq. cms. When Zi and ai are in inch measure, n/ = 0.3132*/i -^ nai. Induction. It a conductor, of length cU, is moved in a magnetic field (of strength 3C) with a velocity, t; (the conductor making the angle a with the direction of the lines of force and the direction of motion being at the angle with the plane passing through the conductor in the direction of the lines of force), the induced electromotive force, dE—SCv sin a sin ^dl, or, J^= / 3Ct> sin a sin 0dl. When a = /9=90'*, E is a. maximum and is equal to JCrZlO"* volts, when v is stated in cms. per sec. and I in cms. The mean E.M.F. of the armature of a two-pole dynamo, JS? = ^ volts, where * is the total number of lines of force flowing between the pole-faces, n the number of active conductors on the armature, and N =r.p.m. In a series-wound multipolar dynamo, E — ' ^ , volts, and in a multiple-wound multipolar dynamo, ^=*iniNriO~s-i-60, where *i=no. of lines flowing between one pair of poles, and p»no. of pairs of poles. The Direction of Currents, Lines of Force, etc. The lines of force in a magnet or solenoid flow from the south pole to the north pole and return outside to the south pole. The north pole of a magnetic needle when brought near a magnet points in the direction of the lines of force. To determine the direction in which a current flows in a conductor, place a compass underneath it. If the north pole of the needle points away from the person holding compass (who is at one side of the con- ductor) the current is flowing to his right. To find the direction of a current flowing in a coil, find the north pole by means of a compass, the north pole of which will be repelled by the north pole of the coil or magnet. Then place the right hand on the coil with tne thumb (at right angles to the extended fingers) pointing in the direction of the north pole and the current will be flowing in the direction in which the fingers are pointing. If the direction of current is known, the north pole may be similarly determined. The positive ( + ) pole of a generator of electric current is the one from which the current flows into the external circuit. In primary batterieu the zinc is negative, copper, carbon, etc., being the positive poles. 134 ELECTROTECHNICS. Direction of an Induced Current. — If the letter N be drawn on the face of a north pole and a conductor (parallel to the vertical lines c^ the letter) be moved past the pole in a plane parallel to the pole face, the direction of current flow will be determined by the motion of the point of intersection (projected) of the conductor and the oblique line in the letter N. Thus, if the conductor moves from left to right, the point of intersection moves from above to below, which indicates the direction of the induced current. ELECTRO-MAGNETS. Traction or Lifttng Power, If a bar of iron be bent into the shape of the letter U and coHs of insulated wire are wound upon the limbs, the electro-magnet thus formed (when a current is flowing through the coils) will have a lifting or holding power on each limb of P (in lbs.) =B^a-i- 72,134,000, where B=no. of lines of force per so. in. of iron section and a is the area of one pole-face of the magnet. The number of ampere- turns is the coils necessary to produce the pull, P= 71/ =2,661 — Vp-s.^ where I is the length of the magnetic circuit in inches and /i the permea- bility. B may be taken at 110,000 for W. I. and mild steel. The above formula is used when the keeper or armature is in contact with the pole-faces. If the keeper (by which the weight to be lifted or held is supported) is distant z inches from the pole-faces, then, nI = 2zXB X 0.3133. If the iron is of good quality and far from saturation the number of ampere-turns required to force the flux through the metal part of the circuit is small enough, comparatively, to be negligible, and the formula value, which is the ampere-turns required to force the flux across the air- gaps, may be taken as the total. Fig. 2a. An iron-clad magnet which may be similarly considered is shown by the part ABC in Fig. 28; the cyhn Irioal core C, however, should extend through the coil to the plane AB. Pluneer Electro-Magnets. Fig. 28 shows an electro-magnet of the iron-clad or jacketed type, which is provided with a movable plunger or core, D, an inner projecting core, C, and a guide or **stufl5ng-box," E. The air-gap is indicated by z and x i.s the stroke of the plunge" or its range of motion, which must be less than 2 in order to meet t-ie conditions imposed in designing for certain soecified pulls at the beginning a'^' end of sf rokp Pull in lbs.=P = aB2^72. 134,000 (1). fi = n/-^0.31.332 (2). Maxi-' mum pull (at end of strojce) = Pg. Minimum pull (at beginning of stroke) = Pi, Let y = Pg-^Pi = B£ Bi^ then -^ and Bi=Bg-i-\^ (3). At ELECTRO-MAGNETS; 135 the beginning of stroke, Bi;sX0.3133— n/, and, at the end of stroke, 0.3133Ba(a— a;)=-n/, consequently -^"Bg+Bf^y' and z'=xy/y'-*-y/y-l (4), Z—-X Let d-=diam. of core in in., then, a = 0.7854^2, and, from (l),d— 9,580>^Pi + B{ (5), which determines (2 if B/ is fixed apoo. If d is fixed. Bz-9.580'/Pr^<f(5o). Irom (2). n/-3.0002'/Pr+d (6) which allows the calculation of the ampere-turns if d has been decided upon. Length of winding bobbin in in.^L; available winding depth in in. »- T ; mean length of one turn in in. — M\ sectional area of coil m sq. in. » hT\ winding volume "■ MZ/T*. If the actual permissiUe current density over the gross section is &, then nl'^^LT, or, LT-^nl+fi (7). For momentary work fi may be from 2,000 to 3,000 amperes, if the magnet is well ventUated and provided with radiating surfaces. For continuous use over_several hours, ^9— 300 to 400 amp. From (6) and (7), T — Z,OOOz^Pi-*-0dL. Assume that L— «, then, if i9 is taken at 2,000, T— l.S'^/Pi + d (9). M = n(0.25+d+T) (10), assuming that the core of bobbin and clearance add 0.25 in. to d. Current density in copper (amperes per sq. in.) =a; diam. of bare wire = ^, do. of insulated wire«» di; R^ resistance in ohms; ri» resistance in ohms per inch of wire; «*» sectional area of wire in sq. in.; o*' space factor, =• total copper section -4- XT*; V— volts at terminals; u?— watts used; VI^I^R. /9» resistance in ohms per cu. in. of coil space. If / is given, rd-hli^n; fi^nl-i-LT; p — 0.8o;9-«-(/2xi0«); «-/+a, and V=-u;+/. If Fis gi ven, /=u ;-H V; n- V-i-MnI, or.fiperl.OOO ft.- 12,000F-J- Afn/; 3 ^O.OOW Mnl-hV; £-0.8Mn/-*-FX10«; a^0.7S54d'-i-di^; LT-'tu-ho, and Af=417d«J+aaVPz. If a solenoid is provided with an ample and well fitting iron guide or stuffing-box at the end at which the plunger enters the coil, the effect of its presence will be to bring up the field at the point when the plunger is just entering to the intensity which exists at mid-length of the solenoid. The maximum pull (when plunger has reached the bottom of the coil) is one-quarter of that calculated from equation (1). If the permeability of the iron is known, B can be found from tables. Calculation of a Planner Electro-Masnet. A number of designs should be made and the ccQculations tabulated in order to determine the most economical one, in weight of copper and in watts required. Example: It is required to design an iron-clad coil to give an initial pull of 25 lbs., increasing to 100 lbs. at the end of a stroice or range of 2 inches, E.M.F. suppUed being 100 volts, for intermittent work. Pa-100; P|-25; x-2; J/-4; v^=2; « = 4; Vp/«5. .n/d=3,000X 4X6-60,000; i3*d-9,580X 5 -47,900, and Bjy-47,900X 2-95,800. . Trial Values. . d in inches - 1 2 3 4 nl - 60,000 30,000 20,000 16,000 Bi = 47,900 23,950 16,966 1 1,975 Bg = 95.800 47,900 31,932 23,950 Let i9-2,000, a-0.6: then, a-4,000. Then, for 7'-<3 in. (which will allow from 10,000 to 30,0(X) amp.-tums per inch length of coil, if properly ventilated) d in inches — 1 2 3 4 LT -30 15 10 7.5 /. - 10 5 4 3.75 T ""3 3 2 6 2 M.". '. .' .' .' .' .' ! .* .* .' - 13. 36 16. 5 18 .' 07 19 . 66 MLT, = 400.8 247.5 180.7 147.4 d - .09 .07 .06 . 0543 8 - . 006413 . 00396 . 00289 . 002357 / - 25.65 15.84 11.56 9.428 n -2339 1894 1730 1591 u -2565 1584 1156 942.8 Copper, lbs = 63. 73 39. 36 28. 73 23. 44 136 ELECTTKOTECHNICS. fin [f it is desired to use metric units (1) should read: Pull in kilograms » 5^.24,655,000, and (2); i3=n/ +0.7962, where B is the flux density in lines per sq. cm., a=area in sq. cm., and 2 = gap-length in cm. The foregoing is an abstract from a paper presented at the International Electrical Congress, St. Louis, 1904, by Prof. S. P. Thompson, F.R.S. (1) and (2) may be combined into the form P==a(7i/-*- 2,6602)2. Mr. C. R. Underbill (E. W. & E., 5-20-05) states that this expression is at best incomplete and offers the following formula: Pull at any point la, P=a(n/+2,6602)2+aZaPe(n/-A;)-J-0.4L(10,000-ifc), where L=length of winding or solenoid, /a = distance plunger has entered the coil, from end of winding, Pc and k having the values given in the succeeding paragraph on "Solenoid and Plunger." Solenoid and Plunger. The ampere-tums (n/) required to produce a pull of P lbs. on a plunger of Swedish iron may be calculated from the following formulas, which are due to C. R. Underbill (E. W- & E., 5-13-05): n/=riO,OOOP-A;(P-P.)]-t-Pc; ^-0.01>/n/; d=0.1128>^; where Pc^* pull in lbs. on 1 sq. in. of plunoer section when n/» 10,000, A = area of section in sq. in., and A; = an empirically determined factor. Pe and k are to be determined from the following formulas which have been derived by the compiler from curves in the original article : Pc — i 102.73 + 0.2105Z») -*- (1.684+L); Ar = (66,000-3,000L)-5-(/. + 18), where L = length of plunger (and generally that of solenoid) in in. In calculating, add 10% to P desired, and the range through which it will be practically uniform will=»0.5X. Example: For a pull of 30 lbs. over 5 in., P=30X1.1=33; Z/ = 5X2« . 10 in.; Pe-8.973; A; = l,285.7; n/ = 33,334; A = 1.83 sq.in.: d= 1.523 in. From an examination of the data emploved by Mr. Underhill the compiler has deduced the following formula, which is much simpler and sufficiently accurate; n/=96P(L+l). CONTINUOUS-CtJBBENT DYNAMOS* Connections and Flow of Current. Series-wound dynamo: Arma- ture—field magnets— external circuit— armature. Shunt-wound dynamo : Armature- { f^iern^oSSclit ! — »""«»*««>• Compound-Wound dsmamo, short shunt : Anmofiir^ ( scrics maguct coils — external circuit I «-«»o*«iv. Armature- } ^^^^^ ma«net coils ) —armature. Compound-wound dynamo, long shunt. Armature-^ries coils- 1 ^JSTSi^fcoiU I -^'™»t'™- (In the brackets the current divides between the paths in the upper and lower lines inversely as their respective resistances.) Efficiencies of Dynamos. Let ^=E.M.F. in volts; /»» armature current in am(>eres; c = volts at terminals of dynamo; t — amperes in ex- ternal circuit; 18 = amperes in shunt coils; £7 = total watts; «i=- useful watts in external circuit; £i~ armature resistance; £2 =» series-coil re- sistance; fis= shunt-coil resistance; r— resistance of external circuit (all resistances in ohms). -Y—r.p.m.; ]}«=» electrical efl5ciency==et-4-^/; 17^= commercial efficiency =-ci-*- 746 XH. P. Then for magneto and sepa- rately excited dynamos, ij. = e-*-^=r-^(r+fii); for series-wound dynamos, i),=^e-i-E=r-i-ir + Ri+R2)\ for shunt-wound machines, -^—ei-^EI^ iV -5- (iV -H U^Rz + /2fti ) ; for compoimd- wound , short-shunt dynamos, iit=ei-^EI = x^r-^{i^{r+R^+iB^Rz+I^Ri]', for compound-woimd, long- shunt dynamos, Jie = ei-i- EI = 'Pr-i-[vh'+P(^R^-\-R2)-¥'u^Rzl The Armature. Let ni = numi)er of coils on armature and n2= number of turns per coil; then, the number of active conductors for a ring armature, riQ — nin^, — for a drum armature, no = 2nin2. The E.M.F.==*7io«10~*H-60. where « is the number of revolutions jjer minute. The cross-section of the armature iron, a=^<P-^B, where B= 10,000 to 16,000 lines per sq. cm. (66,000 to 100,000 lines per sq. in.) for soft charcoal-iron discs, the lower CONTINUOUS-CURRENT DYNAMOS. 137 values for multipolar machines. (For the air-gaps take only about 40% of these values.) In order to avoid sparking Kapp states that B should equal or exceed 2,500(n/)i4-((n/)i — (n/)2] for ring armatures (for drum armatures take 60% of value for ring armature), where (n/)i is the number of ampere- turns required to overcome the reluctance of the air-gap, and (n/)2 is the number of back ampere-turns of the armature. [(n/)2 = no. of conductors included by one pole-face X current strength in amperes.] The current in the armature sets up a magnetization opposed to that of the field magnets, and the effective field is the resultant of the two. The external diam. of armature. dt = k^EI-^NX (J. Fisscher-Hinnen), where ;i = length of armature -s-c?«. For ring armatures. A; = 11.5 when cKt is in cm. and =»4.6 when d, is in inches; i=0.5 to 1.4. J\r = r.p.m. For drum armatures, A = 10 (d« in cm.), and =4 (</« in in.); ; = 0.75 to 2.8. The diam. of hole in armature disc, di^ (0.7 to 0.8)rf« for ring armatures and (0.3 to 0.6)d, for drum armatures. The peripheral speed, 8, should not exceed 50 ft. per sec. (15 meters) for small armatures, and 80 ft. per sec. (25 m.) for large armatures. (In exceptional cases it may reach 100 ft. per sec. as for steam turbine generators.) The length of an armature, /, =(1.05 to 1.2) . .. for smooth-surfaced armatures. For toothed armatures, </. is the diameter at the bottom of the teeth. The cross-section of the armature conductors is determined by allowing 600 to 800 circular mils per ampere. To find the diameters of cotton-covered wires, add the following values to the diameters of bare wires: P Single- Double- viauge. covered. covered. to 10 0. 007 in. 0. 014 in. 10 " 18 .005 ** .01 ** 18 and upwards .004 ** .008 '* In order to avoid eddy currents armatures are made up of discs of sheet metal (0.015 to 0.025 in. thick) which are insulated from each other by sheets of tissue-paper, rust, or by japanning their surfaces. A sheet of good insulating paper-board is inserted at about every half inch of length and open spaces are left about every two inches to provide for ventilation. The loss in watts due to eddy currents = a4.5 to 16.5)Xk(Btp)^X10-^\ where A;'='cu- cm. of iron in the core, ^ = thickness of discs in mm., and p=»no. of periods per sec. Armatures, when adequately ventilated in order to avoid injurious heat- ing, and running at peripheral speeds of from 30 to 50 ft. per sec, reouire from 6 to 7 sq. cm. (0.75 to 1.08 sq. in.) of external surface from which to radiate the heat of each watt wasted therein. (Kapp.) The permissible rise in temperature (40® to 50° C, or 75° to 90° F^ is t (in degs. C.) = 85.25 Pr-i-/S(l+ 0.0305a); t (in degs. F.) =153.45Tr-i- iS(l+0.0305«), where Tr= watts lost in armature, iS = outside surface of armatiu^ in sq. in. and » = peripheral speed in ft. per sec. In order to avoid fluctuations of E.M.F. and the sparking due to self- induction, the number of coils on the armature should never be less than 30, and as much larger as is consistent with the design. The E.M.F. between two consecutive segments of the commutator should not exceed (45 — 0.2/) volts for currents under 100 amperes, and 20 to 25 volts for heavier currents. The radial depth of the windings on an armature should not exceed one-tenth of the core diam. so that tne distance between the core and the pole-faces may be as small as possible. The core should be well insulated from the windings by means of press-board, canvas, etc. In driving the armature, each conductor opposes the motion by a re- sistance, or "drag," F (in kilograms) =/fi/-*-9.81Xl0^ where / = length of conductor in cm., and iB = induction per sq. cm. F, lbs. = ZB/ -J- 11,303,000, where I is in inches and B in lines per sq. in. / = current in amperes). The wires should therefore be secured against motion relative to the core surface. In small armatures the frictional resistance of the wind- ings is sufficient, and in toothed armatures the teeth provide backing for the wires. Ilie coils must also be held in place against the action of cen- 138 ELECTROTECHNICS. trifugal force by bands of German silver or steel wire which axe tigiitly wound around the exterior of the coils in the plane of revelation, secured by soldering or brazing, and insulated from the coils by a layer of mica from 0.012 to 0.025 in. thick. The band wires are from 0.04 to 0.08 in. in diam. and the bands are from 0.6 to 1.2 in. wide. The clearance between the bands and the pole-faces should be from 0.08 to 0.2 in. Field Magnets. In order that a magnetic flux of ^a lines may pass through the armature core there must be a certain number of ampere- turns on the field magnets. The dynamo is to be considered as a closed magnetic circuit through whose several parts (armature core, air-gaps, magnet cores, and yoke) the lines of force flow. For each separate part, g^^^CR, and, as 5-»0.4}m/, the ampere-turns n/=0.7968*(R. If I is the length of the mean path of the lines of force in each part in cm., and a the cross-section of each part in sq. cm., then, for the air-gaps, n/ «»0.79585i; for iron, n/ =0.7968///, where B = *-^a, H-'B-^n, and «— l~for air. In the following table B is given as a function of 0.795SH='H\ so that n/^H'/, i.e., H' is the number of ampere-turns required to force B lines through 1 cm. length of iron. Ampere-turns for 1 cm. length of mean path of lines of force (£/'). n < 1 per sq. cm. per sq. in. Sheet metal. Cast steel. W.I CI. 2,000 12,900 0.35 0.65 0.5 3 4.000 25,800 .75 1.3 1 6.5 6,000 38,700 1.1 2.1 1.7 18 7.000 45,150 1.25 2.65 2 31 8,000 51,600 1.4 3.25 2.35 48 9.000 68,050 1.6 4 2.8 72 10,000 64,500 1.75 5 3.4 97 11,000 70,950 2 6.5 4 133 12,000 77.400 2.7 8.6 5 176 13.000 83.860 4 12 7 232 14,000 90,300 6.5 18 12 15,000 96,750 12 26.8 21 16,000 103,200 21 40.6 40 17,000 109,650 40 58 72 18,000 116,100 71 93 120 The above values are for first-quality American metals. (Sheldon.) To find the number of ampere-turns per inch of length, multiply values in table by 2.64. The value of /x may be found from table, it being equal to 0.7958B-J-/7'. For high densities such as are found in the teeth of sheet-metal armature discs, B per sq. cm « 19 ,000 20,000 21,000 22,000 23,000 //' per cm = 100 184 320 800 1.450 Calculation of the Ampere-turns of a Dynamo. Armature: #«, iia, and Ba are determined by the design of the armature : la is approximately measured from the dimensions of the core discs, and, the value of Ha corresponding to Ba being taken, {nDa — H'ala- If tne armature is toothed, a special calculation is necessary; at is then the cross-section of the iron in the teeth before one pole-face and should be of .such an area that Bt is about 19,000 per sq. cm. Air-gaps: *^==*a; /wr='2J, where ^ = distance from armature core to pole-face; aair = >l6, where ;i and 6 are respectively the length of the arc and the breadth of the pole-faces. B^, = *,!,■*- 0.1, and (n/)ai,= 1.5916B.i,^. ^ , . , . Field: — Not all of the flux in the field magnets pa.sses through the arma- ture, a part being lost through leakage between the poles. This stray field amounts to from 10 to 50% of the total flux and the field flux must therefore be accordingly greater than that required by the armature. The number of lines of force in the field, *m«=c*o. where c has the following ^ues: CONTINUOUS-CURRENT DYNAMOS. 139 Capacities of Djmaraos in Kilowatts. Typea of Field Magnets. ^ ^^ ^^^ 3^^ goo 1.000 2,000 Upright bipolar, yoke at top, o«1.65 1.45 1.3 1.2 Same, — yoke at bottom . . . c-=l. 45 1. 28 1. 2 Vertical double magnet (Man- chester) 1.8 1.55 1.4 Radial outward multipolar 1.5 1.32 1.25 1.2 1.18 1.16 1.15 Same, but with inner poles 1.4 1.3 1.22 1.18 1.15 1.12 1.1 Axial multipolar 2 1.7 1.65 1.45 1.4 1.35 1.3 The sectional area, am, is calculated in accordance with the permissible /?m. which for C.I. is from 5,000 to 10,000 lines per sq. cm (32.000 to 64,000 n-r so. in ). and for W.I. and steel is from 10.000 to 16,000 per sq. cm. (65,000-to 103,000 per sq. in.). Then, (n/)«» = FWm. If the cores, yoke, and pole-pieces are of different materials, a separate calculation of the (n/) for each should be made and their sum taken. On account of the reaction of the armature current upon the field the latter is weakened and it is therefore necessary to add from 7 to 15% to the number of ampere-turns. This amount may be approximately calculated by the following formula of Kapp: Let 9= the shortest distance between two pole-pieces; then, (nI)g=^noIg+it(de+2d), where no*=No. of active conductors on the armature, de= external diam. of armature in cm. and ^=air-eap between armature core and pole-face in cm. Finally, the total number of ampere-turns required in the field magnets, n/ = (n/)« + (n/)ri,H- (n/)m + (n/)(7 = T„in„i. In series machines im == / or a fractional part thereof. In shunt machines im is determined by the loss permissible in the coils for excitation. The mean length of one turn Lm (in meters) is previously calculated; the resistance, rm is calculated with regard to the permissible drop, em, and rffi==em-i-im. The cross-section of the magnet wire in sq. mm. is then, aw = LmnI-i-55em. The current density in the field coils should not exceed 2 amperes per sq. mm. (1,300 amp. per sq. in.). In shunt machines from 20 to 40% of the field resistance is used for regulation. Kapp states that from 10 to 16 sq. cm. of outside coil surface (1.5 to 2.5 sq. in.) is necessary to radiate the heat of each watt lost in the coils. The rise in temperature (25° to 35*» C.) t (C*>)-=(280 to 320 )Tr-i- surface in sq. cm. =(43.4 to 49 .6 )Pr-*- surface in sq. in. Also, <(F.)=»(78 to 89)W-i- surface in sq. in. Tr=»No. of watts. Fields should be massive, compactly designed with well fitted joints, and in large sizes should be of W. I. or steel as C. I. requires too great a weight of copper. A circular section should be preferably adopted, sharp edges and comers being avoided, as they tend to increase the leakage. Sparking may be decreased by so boring and adjusting the pole-pieces that the tips are farther distant from the armature-core than are the points midway between the tips. Eddy currents in pole-pieces mav be avoided by slitting the faces in planes at right angles to the axis of rotation of armature, or by construct- ing the pole-pieces of sheet-iron laminations. The Commutator segments should be from 0.25 to 0.4 in. thick, made of cast or hard-drawn copper, and insulated from each other by thick- nesses of from 0.025 to 0.04 in. of mica. The segments should have a length of about 1.25 in. for each 100 amperes of current, when copper brushes are used. When carbon brushes are employed, length should be from 1.8 to 2.5 in. per 100 amperes. Brushes. Copper brushes should have a surface of contact with the commutator of from 0.0055 to 0.007 sq. in. per ampere, brass brushes from 0.008 to 0.01 sq. in. per ampere and carbon brushes froom 0.018 to 0.038 sq. in. per ampere. Each brush should cover about 1.5 segments and should be from 1.5 to 2 in. in width, excepting in small machines, where lesser widths are used. Armature Shafts should possess unusual st iffness in order that vibra- tion may be avt)ided. Diam., d = c<^H.F.-hN, where c-«=16 to 23 when d in in cm. and 6.3 to 9 when d is in inches. The Weight of a Continuous-Current Dynamo in lbs.=386i^it where /C = output in kilowatts at 1,000 r.p.m. (Fisscher-Hinnen). Abou*- 140 ELECTROTECHNICS. 0.2 of this weight is in the armature If the dimensions of a dynamo are multiplied by m, the output will be increased m^-^ times, with equal circumf., speed of armature, equal heating, etc. (Kapp.) The Design of L«arg;e Multipolar Dynamos. The foUowingmatter, abridged from a series of articles by H. M. Hobart, M. I. E. E. in Technics (London, Jan. to July, 1904), will serve as an illustration of the methods employed in the design of large continuous-current generators. A 400- kilowatt machine (550 volts, 730 amperes) with 8 poles (100 r.p.m.) is taken as an example. E.M.F.=4riVMXlO-* (1), where r=no. of armature turns in series between + and — brushes, iV^= cycles per sec. or periodicity of reversals of flux in armature core, 3f — magnetic flux linked with coils in armature. The armature has a multiple-circuit wind- ing, there being 8 paths through it for the current. The external diam. £) = 230 cm. The polar pitch t-;cX230+8 = 91 cm. Gross length of armature between flanges, Xg^40 cm. There are 8 ventilating ducts, each 13 mm. wide, and 10% of the net length is taken up by insulation. .*. Net length between flanges, Xn=27 cm. The mean length of one arma- ture turn (lap winding) «-3r + 2>ln'= 327 cm. Total number of armature slots '"264, and, as there are 6 conductors per slot, the total number of face conductors — 264X6^1,584, and the total number of turns » 1,584 + 2 — 792. Turns in series between brushes = 792-*- 8 = 99. Total length of conducting circuit between brushes = 327X99—32,400 cm. Cross-section of one conductor— 2.4 mm.XlS mm. = 0.312 sq. cm. Total cross-section between brushes (8 conductors in parallel) =0.312X8 — 2.5 sq. cm. Arma- ture resistance at 60<* C. = 32,400X0.000002 +2.5 = 0.026 ohm. Voltage drop in armature —7/2 = 730 amp. X 0.026 ohm = 19 volts. Drop at brushes —2 volts (ranges from 1.2 to 2.8 volts). Assumed drop in compound winding— 3 volts. Total drop in machine = 24 volts. Internal voltage — 650 + 24 - 574 volts. JV = ( 100 + 60) X (8 + 2) - 6.67,and r - 99 ; substituting these values in (1), Af = 21,800,000 Unes. Core loss due to hysteresis and eddy currents: Watts per kilogram of weight — 2.54 X^riodsXkilolines per sq. cm. + 100 (2). If the internal diam. of armature disc — 140 cm., gross area of disc = -j (2302— 140^)=. 26,100 sq. cm. Area of one slot (3.3 cm. deep X 1.23 cm. wide) — 4.06 sq. cm. Area of 264 slots— 4.06X264 = 1,100 sq. cm. .*. Net area of disc -26,100 -1,100 -25,000 sq. cm. Volume of iron in core- 25,000 X 27(=jl^)— 675,000 cu. cm.— 5,250 kgs. The core is 42 cm. deep below the slots, consequently the cross-section of core — 42X27 — 1,135 sq. cm., but, as the field flux divides as it enters the core and flows both to the left and right, twice this value, or 2,270 sq. cm.,— area of core, and the flux density in core will then be 21,800,000+2,270-9,600 lines, or 9.6 kilolines. The core loss in watts per kg. from (2) - 2.54 X 6.67 X 9.6 + 100 - 1.7, or for the entire core -5,250X1.7 =8,900 watts. Watts per square decimeter of external cylindrical surface of armature: The over-all length of armature may be taken as L— iU-l-0.7T=104 cm. Surface = ;cDL-ffX230Xl04 = 75,000 sq. cm. -750 sq. dm. The loss in the copper of armature conductors = /2JK = 7302X0.026 — 13,100 watts, and the total armature loss — 13,100+8,900 — 22,000 watts. Watts per sq. dm. — 22,000 + 750 = 29.4, for which value the rise in temperature will not exceed SO^'C. The M-M.F. corresponding to 9,600 lines per sq. cm.— 4 ampere-turns per cm. of length for sheet iron. (This value for English metal is much nigher than that given in preceding table of values for H^ of American sheet iron.) The length of path in armature per pole — 42 cm. .*. 42X4 — IdS'^anipere-tums per coif— M.M.F. for armature core. Tooth density and the corresponding M.M.F. : r- 91 cm.; arc of i>ole- face = 61 cm.; .*. pole-arc =0.67t. There are 264+8—33 teeth per pole, 67% of which (22.2) lie below the mean pole-aro. Allowing 10% for "spread '' of flux, the total number of teeth tnrough which the flux passes — 24.4 Diam. of armature at the bottom of slots = 223 cm., and circum- ference at same diam. = 700 cm. 700 + 264 = 2.66 cm. — tooth pitch at bottom of slots. Width of slot is taken — 1.23 cm., leaving width of tooth => 1.43 cm. 24.4 teeth X 1.43 = 34.8 cm. at roots. 34.8 X^n or 27-940 sq. cm. — area of magnetic circuit at roots of teeth for one pole, and the apparent flux density =21,800.000+ 940 =23 .200 lines per sq. cm. This apparent CONTINUOUS-CURRENT DYNAMOS. 141 density must not be employed, but a corrected one which varies according to the ratio of the slot width (a) to the tooth width (6). In this case a-s-& = 1.43-»-1.23 = 1.16, and by interpolating in the following table the corrected density is foimd to be 21,800 Unes per sq. cm., requiring 640 amp.-tums per cm., or, as length of tooth = 3.3 cm., 2,100 amp.-tums per coil for the teeth. ^iSSSy! ' Corrected Density. . a-«-6- 0.6 0.75 1 1.25 18,000 17.400 17,700 18,000 18300 20,000 18,800 19,200 19,500 20,000 22,000 20.000 20,400 20,700 21,300 24,000 21,000 21,500 22,000 22,400 26.000 22.000 22.600 23.000 23,400 28,000 23.000 23.600 24,000 24,500 30.000 23.700 24.600 25,000 25,500 Air-space or gap: Area of pole-face = pole-arc Xiflf= 61X40 — 2,440 sq. em. Average pole-face density ="21, 800,000 -s- 2,440— 8.900 lines per sq. cm. Ampere-turns per coil— 0.705 X average density X length of gap in cm. = 0.795 X 8,900 X 0.9 = 6,400. Magnet cores and yoke: Cores may be of cast-steel, W. I., sheet metal, or 0. I. ; yokes of C. I. or cast steel, — occasionally of sheet metal. Densities for large machines are kept around 14,000 to 15,000 hnes per sq. cm. for cast steel and at about 16,000 for W. I. In smaller machines lower values are taken. The flux for the cores and yoke must be greater than that in the air-space and the armature (or account of leakage or dispersion of the lines of force when leaving the poles), and the armature flux must be therefore multiplied by a leakage factor, or, as it is called by Prof. S. P» Thompson, a dispersion coefficient, which ranges from 1.1 in very larg9 machines to 1.25 in small and compactly designed ones. In this examine it is taken at 1.13 and the flux in field is therefore 21.800.000X1.13 — 24.600.000 lines. The core density is then 24,600,000 -s- 1 .630 - 15,100 lines for cast steel, the core being 45.5 cm. in diam. and having an area of 1.630 sq. cm. The yoke is of cast steel and is designed for 9,000 lines per sq. cm., and has therefore a total sectional area of 2,772 sq. cm., but as the flux divides after leaving the core and flows to the right and left, this value is seen to be twice the actual cross-section, which is 1,386 sq. cm. The length of the path of flux in the magnet core is 50 cm. and that for the yoke and pole-shoe is 73 cm. (=i of the total length of path in the yoke between two consecutive cores). The number of amp.-tums per cm. length of core at 15.100 lines — 28, and for total length of 50 cm. — 1,400 amp.-tums. The amp.-tums per cm. of yoke length at 9,000 hnes — 6 or for total length of 73 cm. —440 amp.-tums. Total ampere- turns per coil for 574 volts, at no load; Armature core below the slots 168 teeth 2,100 Air-space 6,400 Magnet core 1,400 Yoke 440 Total 10,508 The direct demagnetizing effect of the armature winding when a current is flowing is very considerable and increases the more the brushes are displaced from the mechanical neutral point. This effect may be closely calculated from the formula: Amp.-tums per field coil to overcome demag- netizing component of the armature field =0.0175/P7*a, where / — amperes per turn in armature coil, 7^0 = armature turns per pole, and P — percentage of polar pitch by which the brushes are set in advance of the neutral point. In this example, / — 730-^-8=91 amp., 7*0 = 99. and. if brushes are set ahead 15 segments of the commutator, P— 15X100 -»- 99 — 15.2%, and 0.0175/Pra = 2,400 amp.-tums. The distortional component of the field set up by the armature current may be taken at 10% of the total armature field per pole — 730 amp.X 142 ELECTROTECHNICS. 99 turns X 0.10-*- 8 =900 amp.-turns. Therefore for 560 tenuinal volts (674 volts internal) at full load are required: Amp.-turns for saturation at no load 10^508 '* to counteract demagnetization .. . 2,400 * * ' * " distortion 900 Total 13.808 per pole (In a two-pole dynamo, if the brushes are set at the mechanical neutral point, i.e., at right angles to the direction of the fiux, the current in the armature will produce a flux at right angles to that of the fields and tending to distortion of the same. If the brushes are set at OO*' from the neutnd point, the effect of the armature current is purely one of demagnetization, the flux it produces being directly opposed to the field flux. The brushes being generally set at some intermediate point, it will be seen that both distortion and demagnetization have to be considered). At no load and 650 volte the saturation turns required = (550 -h 574) X 10,428X0.93 = 9,300 amp.-turns, where 0.93 is a ffiwitor which approximately allows for the bending of the no-load saturation curve. The shimt coils must there- fore have 9,300 amp.-turns at all loads, and the series coils at full load 13,728-9,300=4,428 amp.-turns. Space factor in winding: — In armatures with voltages up to 1,000 the insulation thickness between the copper and iron should range from 1.15 mm. to 2 mm., — or, for the present design, say a slot lining 0.4 mm. thick and insulation wrapped around coil of about 0.6 mm. The double-covering of cotton on the conductors may be oonsidered as adding 0.3 nun. to the diam. of the bare wire. The ratio of actual copper section to the slot section is called the space factor and should be as nigh as possible, thereby increasing the output of the machine. This factor is higher the fewer the number of slots and is lower the smaller the diam. of conductors used. Space factors for armatures range from 0.3 to 0.5 for round wires and from 0.36 to 0.6 for conductors of rectangular cross-section. Space factors for field coils range from 0.4 to 0.65, a good average value being 0.5. The value 0.65 is used for series coils with large conductors of rectangular cross-section which are woimd edgewise. Calculation of field coils :^-Space factor taken at 0.6 for both Cdils. The length allowable for winding «> 40 cm. (i.e., 50 cm. minus the thickness of flanges, pole-shoe, etc.). Dividing this length in proportion to the number of ampere-turns gives a length of 28 cm. for tne shunt coil and 12 cm. for the series coil. At full load (coil at 60° C.) 10% of the shunt excitation is wasted in an adjusting rheostat in series with the coils. This reduces the voltage from 560 to 500 volts, or 62.5 volts for each of the 8 coils. Allowing 1 cm. for clearance, the internal diam. of coil ■= 46 cm., and assuming radial depth to be 4 cm., the external diam. will be 54 cm., and the mean length of one turn (a) will be 1.58 meters. The watts per shunt coil at 60° C.-0.000176o262-i-A;, where A; = kgs. of copper per coil and 6 = amp.-turns per coil ( = 9,300). Cross-section of shunt coil = 28X4 = 112 sq. cm., which, multiplied by the space factor (0.5) = cross- section of copper in coil=< = 56 sq. cm. Cu. cm. of copper in coil = 56X1.58X100 = 8,900, and, as 1 cu. cm. weighs 0.0089 kg., the kgs. of copper in one shunt coil = 79. Substituting these values in above formula, the watts per shunt coil = 480. The external cylindrical surface of coil = 48 sq. dm., and the watts per sq. dm. therefore = 10, which allowance will not permit a rise in temperature of more than 40° C. Size of wire in shunt coils: — Amps, per coil = watts -s- volts per coil — 480-5-62.5 = 7.7 amp. Turns per coil = amp.-turns^ amps. = 9,300-*- 7 7 = 1 ,210. Ooss-section per turn = t -s- No. of turns = 56 -f- 1 ,210 »= 0.0462 sq. cm. Current density = 7.7 -f- 0.0462 =167 amp. per sq. cm. Diam. of bare wire = 2.42 mm. Watts in 8 coils =3,840. Watts in shunt rheostat =380. .*. Total watts for shunt = 4,220. 0>pper in 8 coils = 630 kgs. Series coils • — These are placed at the end of core nearest the armature. Winding length = 12 cm. Turns = 4,420 amp.-turns -^ 730 amp. = 6 turns! (In this particular machine 210 amp. are diverted through a shunt in parallel with the series winding so that turns = 4,420 -5- 520 =8.5.) The series coils may have a higher current density than the shunt coils, and, if this is taken at 180 amp. per sq. cm., the cross-section of the series turns = ''SO-*- 180 = 4.05 sq. cm. This may be in the shape of a rectangular section CONTINUOUS-CURRENT MOTORS. 143 (4 cm. X 1.01 cm.) and woimd edgewise. Mean length of 1 turn « 158 cm. Weight of copper in one coil = 6 turns XI 58X4.05X0.0080 -34. 17 kgs., or 273.36 kg. for 8 coils. Resistance of 8 coils in series at 60° C. = 8 X 6 X 158 X 0.000002 ^ 4.05 = 0.00374 ohm. Watts lost in the 8 coils, at 60° C. = 7302X0.00374 = 1,993. Reactance voltage: — When a coil carrying a current arrives at and passes the brush, the direction of the current is suddenly reversed. This change should take place sparklessly and the winding should be so designed that the reactance voltage due to the decreasing current at the moment of commutation will be as small as possible at full load, the brushes being set at the neutral point. Reactance voltage = 12.566e (^) (l +0.15 j-V where e= average voltage per coil ( = 550+99 = 5.5 volts), Q = amperes in conductors per cm. of periphery of armature ( = -^ X ^' = 200 amp.) t B = average flux density per sq. cm. of cylindrical surface of armature [ = (8 X 21,800,000) + (28 X 230 X7r)« 8,600 lines], and T + ;n = ratio of polar pitch to net length of armature core (=99 + 27 = 1.49). The reactance voltage, consequently, is 2.42 volts for this machine, which is low enough to permit a practically sparkless commutation. The brushes should be neld against the commutator by a pressure of about 0.1 kg. per sq. cm., and the loss in watts due to brush friction =0.1 kg X section of brushes in sq. cm. X 0.3 X peripheral speed of commutator in meters per second X 9.81, where 0.3=coen. of friction for carbon brushes ( = 0.2 for copper brushes). The current density in brushes ranges from 4 to 12 amp. per sq. cm., — average = 6. Tike IE loss at commutator in watts = total armature current X volts dropped at brushes' (1.2 to 2.8, — average, 2). Efficiency: — The following is a tabulation of the several losses of energy in the generator at full load : Core loss in armature 8,900 watts (constant) ^ , PR ' 13,100 *• (variable) (c) Brush contact lass 1,460 * ' * * Brush friction Iohs 540 * * (consstant^ Friction loss at bearings, estimated. . . . 3,000 ** ** Loss in shunt coils 3,840 ' * " (l7) " ** series ** 1,993 " (variable) Total losses 32,833 watts Output = 730 X 550 = 401 ,500 watts. Total generated = 401 ,500 + 32.833 = 434,333 watts. Efficiency at full load = 401 ,500 + 434,.333 = 92.5%. At half-load, losses = a+d + «+/+K6 + c+/7) = 24,560 watts. Output = 200,- 750 watts, and total generated = 200,750 + 24,560 = 225,310 watts. Effi- ciency at half -load = 200 ,750 + 225 ,3 10 = 89 % . Cost of manufacture. The factory cost of generators of this class is proportional to the product of the diameter of the armature by the "equiv- alent length of one armature turn over the end connections," which latter may be taken = ;i^+0.7t. The factory cost then — iCi>(;j,+0.7T), A being a function of voltage and of the type of machine. For 6 and 8 pole dy- namos of 250 volts, K may be taken at $0.30, and for 500 volts at $0,265 to $0.28. (These values are for material and labor costs and for methods of manufacture obtaining in Fjigland.) The output and speed being decided upon, a series of calculations should be made, the diameter of armature being so chosen that the peripheral speed will vary from 10 to 15 meters per sec. and the total ampere-turns per pole on the armature varying from 4,(X)0 to 10,000. IVom these designs a choice may be made which will be the best compromise on such points as cost, speed, and reactance voltage, all of which should be as low as possible. For a two-circuit winding on a multipolar dynamo armature, where one pair of brushes is used. No. of face conductors = No. of poles X( wind- ing pitch ±2). CONTINUOUS-CURRENT MOTORS. These are generally designed on the same lines as are djmamos of similar types. The revolutions of the armature develop an E.M.F. which is op- ^r 144 ELECTROTECHNICS. posed to the impressed E.M.F. and which is called the counter electro- motive force. Let E = E.M.F. applied at the terminals of motor, c= counter E.M.F., and fi = resistance of motor armature. Then, l~(E~e) H- R ; total watts, W^EI==E\E-e)-^R', useful watts, w.^el'^ e(E -e)-i-R: W—w+I^R (or watts lost in heating), and the efficiency— io-5-fr = c-&-^. Torque = mechanical power in ft.-lbs.-s- angular velocity. Let «u=»2;rX revs, per sec. = angular velocity, r= torque: then, (uT^:^ mechanical power in ft. -lbs. per sec. c/= electrical power of the armature in watts. H.P.= ^ - ;r^,and e/ = 2 nnT X ^ =■ S.52nT, where n = revs, per sec. e - nm#10-«. 550 74o 560 where m = No. of conductors on the periphery of armature and ♦ =■ flux, r at 1 ft. radius =mW + (8.52X10^. If r = resistance of armature, /=<£z£>, and T (at 1 ft. ) = m* (^^) •*- (8.52X108). R.p.m.=eX60 X108-*-m*. Rheostats for Motors. If a motor at rest were directly connected to a source of current, the mains would be short-circuited throuc^ the armature and the abnormal current flowing would speedi^ bum up the armature coils. It is necessary, therefore, to introduce a starting resist- ance into the armature circuit so that only a moderate current will flow through the armature at the beginning of its motion. As the speed (and consequently the coimter E.M.F.) increases, the current strength decreases, and the resistance may be lowered gradually, by steps, and when full speed is attained it may be cut out of the circuit altogether. The following table gives the resistance and ciu'rent-carrying capacity of several metals used m rheostat coils : Galvani?ed Iron. German Silver. Platinoid. Man- ganin. Ohms per ft. 0.0093 .0133 .021 .0363 .0553 .1013 .1446 .3133 .5 B. W. G. B.W.G. Ohm, Amp. Ohms ^p. O^ ^. 8 0.00266 28 0.00566 19 0.008 13.5 10 .00366 21 .00833 14 .0123 10 12 .006 16 .0127 11 .019 7.7 14 .0117 10 .0203 7 .032 4.7 16 .016 7.5 .0333 5 .05 3.5 18 .029 4.5 .0583 3 .089 2.2 20 .041 3.5 .116 2.2 158 1.5 22 .0883 2 .18 1.5 .262 .95 24 .144 1.5 .29 1 .423 .7 Resistance coils should be wound according to the following table, which gives the sizes for maximum rigidity and energy dissipation: Inner diam. of Approx. length Spiral in inches. Coil in inches. 8 1 27 9 to 11 0.875 22 12 ♦* 14 .75 18 15 •* 16 .625 14 17 •* 19 .5 11 20 "24 .375 8 A starting resistance should be so designed that the momentary increase of current due to cutting out a section of same does not exceed a certain predetermined amount. 1 2 3 4 n 0— r— 0— fii— 0— 52— 0— i?3— 0— /2n— -^8 Current flow. In the above diagram r is the armature resistance, Ri, Rs, R^, Rn are the sectional resistances of the rheostat included between toe segments 1, 2, 3, 4, n. Let the E.M.F. of supply ==^; t = current in armature at full load; / = permissible momentary current, and let I^i = k. The re- sistance Ri between segments 1 and 2 should then be = (fc — l)r, ^2= (A — l)tr, i23 = (A;-l)A;2r, and Rn = (k-l)k^-W. In order for the motor to start, the total resistance in the circuit (=r+Ri-\-R.2+R3. . . +Rn) m st be less than E-i-i. To avoid arcing between the segments no secti >n should have a drop of over 35 volts, and R2-Rik - .084 Rz-Rik « .1176 Ra" .1646 i?5- .2305 ««- .3227 ALTERNATINa CURRENTS. 145 if such a section should occur in the calculation it should be divided into two or more sections, none of which have a drop exceeding 35 volts. For motors using about 50 amperes on full, load 7 may be taken as equal to i-hlO amp. For much smaller motors /"-o '<>** t^^® first section and-"-j on the remainder. If the fuU-load current exceeds 50 amp. the momentary rise (/— i) should not exceed 0.2t. Example: Rheostat for a 15 H.P. motor on a 220 volt circuit. ^ = 220; 1 = 15X746-^220=50 amp. Resistance of amiature, r=0.15 ohm. /=» + 10=60 amp. 7+t=ife="1.2. j^-s-i- 4.4 ohms. The sum of all the resistances = rk^, where n = No. of sections in the rheostat =E-i-i. .'. 0. 15^* «-4.4, and, as A = 1.2, n = 18 (18.5 exactly) sections and the resistance of each .section may be calculated from the previous formulas. If the rheostat is designed to start the motor, say on half-load, t = 25 ; /'=z + 10-= 36; /-J-t=ik = 1.4, whence 1.4»=58.66, and n = 12 sections. ^-<-t = total resistance =8.8 ohms. The several sections would have the following values: r - 0.15 ohm R7 =0.4518 ohrn «i= (*-!>- .06 •* Rg = .6325 " ~ -^^ -'■ ■' Rg ^ .8855 •• i?io =1.2307 ohms «,! =1.7355 *• i2i2 =-2.4297 •• Total =8.5 As n is a fraction over 12, the remaining 0.3 ohm (8.8—8.5) may be added to A12. (Ck>ndensed from an article by F. H. Davies, in Technics, April, 1904.) ALTEBNATIXG CURRENTS. Definitions. Alternating currents are those which periodically pass throufh a regular series of changes both in magnitude and direction. Usually the magnitude increases with a certain regularitv from zero to a maximum, decreases with the same regularity to zero, and then similarly to a maximum in the opposite direction and finally to zero again. When a current has experienced such a series of changes (0 to +max., to 0, to —max., to 0) it is said to have completed one cycle. (Symbol '«-~.) There are two alternations in one cycle. The time taken to accomplish one cycle is called a period and the number of cycles completed in one second is called the frequency, or periodicity. The frequency of an alternat- ing current dynamo =piV+ 60, where p= number 01 pairs of poles, and N = r.p.m. The ideal curve of an alternating current and E.M.F. is a sinusoid, or curve of sineo, and is the one assumed for purposes of theoretical dis- cussion, but commercial alternators do not generate strictly sinusoidal pressures. Referring to Fig. 29, E' at any point = i?niM. sin 2nft, where /=frequency, and / = time in seconds. Also, /=/-.>,. sin 2nff. Effective Values. One ampere of alternating current is a current of such instantaneous value as to have the same heating effect in a con- ductor as one ampere of direct or continuous current. Heating varies as 7^ and, therefore, in an alternating current whose instantaneous values vary, the heating effect is proportional to the mean of the squares of the instantaneous_current8, or, I^ = lm^^2. The effective value, therefore is / = 7m-s-v^2, and the effective E.M.F. , E^Em-^^^. The average current, 7»T-=2/m+>r, and the average E.M.F., E„.==2Etn-*-x, The ratio of the effective E.M.F., and the average E:M.F. = -^-5-?^=l.ll V2 ^ (for sinusoidal RM.F.s) is called the form factor. (The subscript m indicates maximum.) Pliase. When the maximum and zero values of E and 7 occur at the .same instant, the current and E.M.F. are said to be in phase. When the current attains its maximum and .zero values at a time later than when the corresponding values of the E.M.F. occiur, it is said to be out 146 ELBCTROTECHNICS. of phase with the E.M.F., or to lag behind the E.M.F. When maxim unt and zero values are reached at an earUer time, the current is said to lead the E.M.F. The distance between any two corresponding ordinates of current and E.M.F. may be measured and expressed in degrees and is called the angular displacement, or phase difference. This angle is repre- sented by <f>. An alternator giving a single pressure wave of E.M.F. to a two- wire circuit is called a single-phai*c current generator. One giving pressure to two distinct circuits (each a single phase), the phases being 90** apart, is a two-phase, or quarter-phase generator. A three-phase machine E;rv 90' VISO* 270* 360- (T 2 3n' Fig. 29. /27( theoretically has three two-wire circuits, the maximum positive pressure on any one circuit being displaced from each of the pressures in the other two circuits by 120°, but, as the algebraic sum of the currents in all three circuits (if balanced) =0, the three return wires of the circuits may be dispensed with. Power In Alternating-Current Circuits. The power, P, in an alter- nating circuit depends on E, /, and 0, and is thua expressed: P = EI cos 0. Cos 4* is called the power factor, it being the number by which the apparent power, or volt-amperes (EI)^ must be multiplied in order to obtain the true power. When E and / are in phase, 0=0 and cos0 = l. Self-induction : — Impedance, Reactance, and Inductance. A cur- rent flowing in a conductor sets up a magnetic field around it ; conversely, when there is an increase or decrease of the number of lines of force cut by a conductor, a current is induced in it, and in alternating circuits it is necessary to consider these self-induced currents. When the rate of change of value of the current strength is greatest (at 0) the self-induced E.M.F. is a maximum, and when lowest (at peak of the sine curve) the E.M.F. is a minimum: consequently, the phase of the self-induced E.M.F. differs from that of the impressed E.M.F. by 90°, or is at right angles to it. liCt an alternating current of / amperes flow through a circuit having a resistance of R ohms and an inductance (self-induction) of L henrys. To maintain the current flow through R requires an effective E.M.F.l Er = RI. The effective value of the E.M.F. of self-induction, Ea, wili be= —2nfLI, the minus sign indicating that it is an opposed, or counter E.M.F. As Er and Es are at right angles to each other they are not to be added, but are to be taken as two sides of a triangle, the hypothenuse of w hich is the impressed E. M.F., jg; w hence, E = ^^Er^+Ea^'= V(/i2)2+(2^/L/)2. and I^E^^R^ + {2nfL)K VijaH.(2;r/L)a is called the ALTERNATING CURRENTS. 147 impedance, or apparent resistance, and {2nfL) the reactance, botbbeinfi^ expressed in ohms (Fig. 30). As Er is the part of the impressed E.M.F. which sends the current through the conductor {Ea being that required to neutralize the self-induction), the current must be in phase with it, and 7 is therefore always displaced 90° from Es. I and Er lag behind E by an angle (0) whose cosine — ^r-*- ^. The inductance of a cou on the field of a generator is: L (in henrys) — ♦ti/lO"^, where * is the total flux from one pole, n the number of turns in coil, and I the amperes of current in coil. Capacity* Any two conductors separated by a dielectric (i.e., insu- lating substance) constitute a condenser. In practice this term applies to a collection of thin sheets of metal separated from each other by thin sheets of insulation, every alternate sheet of metal being connected to one terminal of the apparatus and the intervening leaves of metal to the other terminal. The function of a condenser is to store Up electrical energy. If a continuous E.M.F. be applied to a condenser, a ciurent will flow, — large at first, but gradually diminishing until the metal sheets have been charged to an electrostatic difference of potential equal and opp)o8ed to that of the E.M.F. applied. The capacity of a condenser is numerically equal to the quantity of electricity with which it must be charged in order to raise the difference of potential between its terminals from zero to unity. A condenser whose potential is raised 1 volt by the charge of 1 coulomb has a capacity of 1 farad. The capacity in microfarads of a condenser =C=- 0.000225— ; — , where ^=»area of dielectric between two metal leaves, in sq. in.; n»= number of sheets of dielectric ; t '^ thickness of dielectric in mils ; k — specific induc- tive capacity of the dielectric. i^pRI ^ a E.=RI Fig. 30. Fig. 31. ebonite, 2.2 to 3 ; gutta-percha, 2.5 ; paraf" '" " '^ "- 1.8; kerosene, 2 to 2.6. Values of k: — Glass, 3 to 7 ; ^ fin, 2 to 2.3; shellac, 2.75; mica, 6.6; beeswax, x.a, ml^^xj^lx^o, « t.^ «.«^. If a sinusoidal E.M.F., E, of frequency, /, be impressed on a condenser, the latter will be charged in -r-. seconds, discharged in the next -77 seconds 4/ 4/ and charged and discharged in the opposite direction in equal succeeding intervals. Max. voltage, Em = E^2; max. quantity, Qm^EC^^; quan- tity per second = 4fQm = 4/JS?CV^^= average current, !„., and, as the effective current, /»= \. Imr; I^2itfCE, and E-^-^-jr;!. ^-i^ is called the capacity reactance and is analogous to 2nfL, Circuits containing Resistance and Capacity. In this case the im- pressed voltage, E, must be considered as being made up of Er, — which (tends the current through the resistance, R, — and Et, which balances the counter pressure of the condenser and which is 90** in phase behind the current. Er^RI, and ^«"2^^' " ^^P**^^^ E.M.F, E'-'^/eJ+E? or 7= , —,——_ •• (See Fig. 31.) ^'^-i.lj i 148 ELECTROTECHNICS. CiEcuits containing Resistance, Inductance, and Capacity. This is the most general case. The counter E.M.F. due to 9eIf-induction = 2irfL, and leads the current by 90**. The E.M.F. of capacity react- ance^jr-jpi, and lags behind the current by 90°. These two E.M.F.'s being 180° apart, the resultant reacta nce is their numeri cal difference and the general equation is: ^=^-^V^^-+[2»r/^-2^] • Th© quantity within the brackets indicates an angle of 1^, if positive, and an angle of lead, if negative. If 2}r/L=-2-^, then 7=-^. This condition prevailing, resonance is said to exist, as, at one uistant, energy is being stored in the field at the same rate it is being given to the circuit by the condenser, and at another instant, energy is being released from the field at the same rate as it is being stored in the condenser. Combinations of Condensers. If condensers are connected in series their combined capacity, C-^-j = z r-. If Ci, Cz* ... C* are — -H — —4-— +— - equal capacities, C=— ^. If connections are in multiple, C — Ci+C2H-Cj!H-. . . Cn, and if Ci=Cj = C3=Cn, C = nCi. Combinations of Impedances. If several impedances are to be arranged in series they should be represented by the hypothenuses of tri- angles whose horizontal sides represent the resistances and vertical sides the reactances. The resultant impedance is then represented by the hypothenuse of the triangle whose base = sum of the resistance horiaon- tals of the separate triangles and whose height = sum of the reactance verticals, or, resultant impedance = '^i'ft2 4. 2j;2;r/Z.^2. If the impedances are in parallel, find their reciprocals or admittances. Take any two admittances at their proper phase angle and construct a parallelogram. The diagonal will be the resultant of these two admit- tances in direction and value. This resultant may be similarly combined with a third admittance, etc. The reciprocal of the final resultant admit- tance will then be the combined impedance desired and the direction of the final diagonal will represent the resultant phase. ALTERNATING-CURRENT GENERATORS. Alternators are either single-phase or poly-phase (i.e., more than one phase, — usually two or three). For low potentials the field is stationary, the armature revolving, while for high potentials the field is made to rotate, the armature being fixed. The latter may have a field of radial poles each of which is of opposite polarity to its neighbor, or, it may be ot the inductor type, in which both field and armature coils are stationary, the rotating part being an iron mass called the inductor. This inductor (which carries no wire) has pairs of soft -iron projections termed inductors which are magnetized by the current flowing in a fixed annular field coil which surrounds but does not touch the inductor. The surrounding frame is provided with radial internal projections which correspond to the in- ductors in number and size, and upon which are wound the armature coils. As the inductors revolve the fiux linked with the armature coils varies from a maximum to a minimum, but its direction is not changed, as the annular field coil gives a constant direction of field. Two-Phase Generator. In a two-phase system of winding, if two coils and 4 conductors are used, each coil generates a pressure of i? volts between the two wires leading from it and there is no connection between the two coils. If three wires are used, connected as shown in Fig. 32, the E.M.F.'s between the wires are as indicated in the diagram. {E and / in the figures are taken as the effective E.M.F.'s and currents.) A monocyclic generator (for lights chiefly, but carrying a certain motor load) is a single-phase machine to which is added on thie armature a so- ALTEBNATING-CUBRENT GENEBATOBS. 149 called "teaaer" winding of a section sufficient to carry the motor load, and with turns enough to produce a voltage equal to one-quarter of that of the regular winding and lagging 90° behind same. One end of the teaser winding is connected to the middle of the regular winding and the Fig, 34. other to a third line-wire. A three-terminal induction motor is used, which is either connected directly or through a transformer. Four-Phase, or Quarter-Phase. See Figs. 33 and 34 for the two 150 ELECTROTECHNICS styles of connections. The current in each line in Fig. 33«/, and in each line of Fig. 34 =7-^/27 Three-Phase (Figs. 35 and 36). Fig. 35 shows the Y or "star" con- nection, the current in each line being 7. Fig. 36 shows the A (delta) or mesh connection, the ciurent in each line being 7'v3r Fig. 35. E.M.F. Generated. E„^2y9n-^^-^, where p= number of oU Fig. 36. N , _. . . pairs of poles, ^—flux per pole in maxwells, i\r = r.p.m., and n=- number of in- ductors. The effective E.M.F. = A;A\t, where k is the form factor ( = 1.11 for a sine wave). Also, piV-*-60 = /, consequently ^ = 2.22#n/10-8. If the armature winding is all concentrated into one slot per pole, single- phase, this formula is applicable. If, however, the wires are distributed over the surface of the armatiue in a number of slots the right-hand mem- ber of the equation must be multiplied by a distribution constant, k\^ which varies according to the number of slots on the periphery of arma- ture from center to center of two adjacent pole-faces and the fraction of the latter distance which is occupied by slots. Values of*,. Part of polar distance occu- 1 slot. 2 slots. 3 slots. many slots. pied by slots. 0.1 1.00 0.996 0.995 0.994 0.2 1.00 .986 .984 .982 0.3 1.00 .972 .967 .962 0.4 1.00 .95 .942 .935 0.5 1.00 .925 .912 .9 TRANSFORMERS. 151 TRANSFOBMEBS. The transformer is a device for changios the voltaee and current of an alternating electric system and consists of a pair of mutually inductive circuits (primary and secondary) or coils interlinked with a ma^etic circuit or core. When an alternating voltage is applied to the primary coil an alternating flux is set up in the iron core which induces an alternating E.M.F. in the secondary coil in direct proportion to the ratio of the number of turns of the primary and secondary coils. The manietic circuit or core is made up from laminations of sheet iron or steel. Two general types are used: I, the core type, whicli is built up from laminations, each of which is a rectangle, with a similar but smaller rectangle stamped out from its center. These laminations are bound together with the holes corresponding and coils are wound on two^ opposite limbs. II, the shell type, which is similarly assembled, but in which each lamination has two rectangular holes stamped out. The coils are wound on the central limb formed by the bridges or cross-pieces between the rectangular holes in the laminations. Laminations are about 0.014 in. thick and are insulated from each other by shellac, tissue paper, etc., in much the same manner as are the discs in armature cores. (See Fig. 37, the coils being wound on the limbs marked a.) .■• Volts induced in transformer coil, ^=4.447'. #/10"*, where 7* —total number of turns of wire in series and /= frequency, in cycles per sec. Eddy current losses. — Watts per cu. cm. of core = (</^)210-i®, where t=- thickness of each lamination m mils, and B is in lines per sq. cm. Amperes required to magnetize core to induction B" , - — where 2 » length of magnetic circuit in cms., B= lines per sq. cm., 7*= No. of turns in primary coil, and /£== permeability of the iron in core. The current at no load IB i/CZ 7n . . , , /watts lost m iron\ * r (magnetising current )2 + ( — : r- 1 • ^ pnmary voltage ^ Transformer Design (abridged from articles by Prof. Thos. Gray, in £. W. <fe E., April 23 and 30. 1904). Let a, b, and I be the dimensions in cm. of the cToss-section and mean length of the copper link or coil, and Oi, 6i, and /i be similar dimensions for the iron link or core. Then, total cross-section of coils =- o6 =« A , and cross-section of core=ai6i=i4i. Volume of iron, Vi'-Aili, and volume of coils, v=*Al. (In this discussion the laminfltions are assumed to be rectangular and the wires as being bent sharply at right angles as they turn the comers of the core.) For a core transformer, ab =^ total section of both coils. 2 — 2 (oi -i ha), and li'^2\a+ — \-^i)* In order that I may be a minimum (assuming 152 ELECJTROTECHNICS. At Ai, and ^i to be constants and differentiating), it is found that for this condition r^ — £-r^» a^d t"= I* i » For the least total volume of material in both cores and coils it is found necessary that a^^-^^, ^^^ AUH-Ai) Ajir ^^ ^,^ A+Ai Ai A+2Ai — ^ — -T — ^-^. If the volumes are to have a definite relative value, let vi — nv, and let the corresponding relative value of the areas be: Ai'^xA, When a:-0.5 1 1.5 2 3 4 6 n-0.796 1.086 1.286 1.435 1.637 1.77 1.864 Let the induction per sq. cm. of core*»B sin ott, and the total induction = iiiBsin wt: then, the magnetising ciurent being small, the amplitude of the appliea E.M.F. will (when the transformer is not loaded) be practically equal to that induced by self-induction; consequently, ^ = ni^4iBoilO~*, where ni = No. of turns on primary coil. Let P=full load in watts, /» square root of the mean square of the full-load current in primary coil, and power factor ■= 1. Then, P'^EI-t- ^2, or 1.41P = ^/. Let i» average current per sq, cm. of coil section. The heat generated in the coils wiU then be, approximately, »4t^l0~^, assum- ing the space factor of the coils is 50% (i.e.. one-half of coil section is copper), and the working temperature = 80® C. At full load the heat wasted in the coils should equal that lost in the 18Bi*« core through hysteresis and eddy currents. This heat, ^"""Tnir' ^ watts per cu. cm. per cycle per second. A certain area of raaiatiog surface, «, must be allowed for the dissipation of the heat of each watt, the total surface being S. For ordinary air- cooled transformers « is taken at 30 sq. cm., and at 20 sq. cm. for trans- formers immersed in oil or cooled by artificial ventilation. The following equations and vidues have been derived frcon the foregoing premises: fi««=7.866X10«x(?^)'(-f-)'x^X^' (1).. Total heat dissipated, Hi-=2X18Bi.«t>i^lO-", in watts per see. (4). 2^^"^^«*«"cy; 1 g = iioiai « jxpoeeu B LLTiaOO A Vi Vl* .1-^. * A' , -f -0.25 0.5 1 1.6 2 2.5 3.5 — f-e 3 2 1.66 1.5 1.4 1.285 «a — ^-1.5 Ol 2 3 4 5 6 8 .-^-6.83 4.76 3.46 2.83 2.46 2.22 1.92 (Read thus When x=l; xi— 2, xa=3, and i;«=-3.46, etc.) Example Core transformer; P = 10,000 watt3, JF« 3,000 volts. ^ — 100, «— 1, and from previous tables ri=-2, ——3, —^—n^ 1.086, and a ""3.46. ai V Substituting in (1), (2), (3), and (4), 5 = 2,747 lines per sq. cm., m (primary) -853 turns, o = 10.1 cm., 6 = 2J.2 cm., ai=8.25 cm., 6i»24.75 cm., A --ili TRANSFORMERS. 153 —204.2 sq. cm., t> — 17,600 cu. cm., vi — 19,110 cu. cm., u+n =36,710 en. cm., Hi =218.3 watts. Efficiency » watts output -*■ watt? supplied — (10,000 -218.3) -J- 10,000 =97.82%. If the iron section is taken as one- half that of the coils, ar=0.5, -^-0.796, a:i-3, ^-2, a ==4.76, i; = 15,940 V ' ' ai cu. cm,, t;i = 12,700 cu. cm,, t>H-»i— 28,640 cu. cm., i/i -222.6 watts, and e£f.— 97.74%. or a dissipation of but 4 watts more than in the first case, and a reduction in weignt of one-third. For shell transformers. B«.«-7.866X10m(^)*(^)*(^)^^^ (6), '""if^'T^i^^sl^* ^®^» *'''* n,-108^+xaB^i8 (7). *»■• — ; a = — ■' In this case, where (e.g.) x — 1, and the iron parts cor- ai vi respond to the copper parts in a core transformer, the values of ~ in the table are used for — and similarly those of — in table for — . a a ai Taking the data of the example given, it will be seen that in this case ~ — 2 instead of 3 as for a core transformer. Substituting the various values in (6), (6), and (7), the following values are obtained- jB — 2,896, ni-S13, a-8.22^ 6 = 24.65, ai = 10.07 6i =20.13, 4 "^1=202.7 t; = 18,890, »i-17,400, v+Vi =36,290, /^i = 216.2; eflf. =97.84%, or substantially the same total volume and efficiency as for the core transformer first con- sidered. If the iron section be made equal to twice the copper section, B-3.091, » = 13,060, t>i = 16,400, v + t;i = 28,140 cu. cm,, ^^1 = 226.6, eff. —97.73%. If u-on section = copper section X 5, 5 = 3,770, t>=7,632, n- 13,640, t>+»i -21,000, /fi -260.2; eff.=97.4%. When a transformer is in circuit continuously, but loaded for only a few hours in the day a greater all-day average efficiency is obtained by designing the traiLsformer so that the iron heat dissipation is considerably less than that of the coil at full load* the efficiency, however, is smaller, on full load. In this case the right-hand members of (1) and (5) must be multiplied by — 5-, and those of (2) and (6) by — , where m= total heat m? tn dissipation •*■ hjrsteresis dissipation. If m— 3 (other data as for shell transformer where B — 2.896), then, j?-3,lQ5, »= 21,180, «, = 19,510, v -I- vi -40,690, Hh«=77.9 watts, f/ooppw- 155.8 watts, i/i =77.9 + 155.8 -233.7 watts. Eff. =97.66%. The weight is thus increased about 12% and the efficiency lowered by 0.18%. If the loflid, however, is on only about 6 hours out of the 24, there is a saving of about 600 watt-hours per day. It is assumed in the foregoing work that the coil and core sections are rectangular. If the iron laminations are rectangular and the wires tn the C9US are bent in the arc of a circle when rounding the corners of the iron core (which is the most general construction), then, for a core trans- former,—- r . ^ ; ^=2 (oi+-r+-7-) J ^i-2(o-l-— +2ai) oi b—a b — a \ ai 4 / \ a / All-Day Efficiency. Let y — No. of hours per day when full load is ou ; then ... , _ . FuUloadX y AU-day efficiency-^^^ loss X 24 + copper lossXy+fuU loadXy Magnetic Densities in Various American Transformers: For 25 cycles, B -9,000 to 10,000 lines per sq. cm. (60.000-90,000 per sq. in.). For 60 cycles, B -6,000 to 9,000 lines per sq, cm. (40,000-60,000 per sq. in.) 164 ELECTROTECHNICS. For 125 cycles, 5 = 4,500 to 7,600 lines per sq. cm. (30,000-50,000 per sq. in.). Current Densities. Primary coil, 1,000-1,500 circular mils per ampere. Secondary *' 1,200-2,000 Insulation between laminations is about 10% of total assembled thick- ness; .'. vol. of iron =0.9 X cubic contents. Economic Design. The best economy of first cost may be obtained by calculating several transformers of the same capacity, but with various ratios of copper to iron, plotting the results and balancing the annual interest on the cost of material saved (labor cost being substantially a constant for a given output) with the cost of the extra watt-hours per year sacrificed by cheapening the construction. CONDUCTOBS. Copper- Wire Table, A. I. E. E. 20"* C. Gauge. Piameter. Area. Weight. „T.ength. B.&S. Inches. Circular mils. Pounds per ft. Feet per lb. 0000 0.460 211,600 0.6405 1.561 000 .4096 167,800 .5080 1.969 00 .3648 133,100 .4028 2.482 .3249 105,500 .3195 3.13 1 .2893 83.690 .2533 3.047 2 .2576 66,370 .2009 4.977 3 .2294 62,630 .1593 6.276 4 .2043 41,740 .1264 7.914 5 1819 33,100 .1002 9.98 6 .1620 26,250 .07946 12.58 7 .1443 20,820 . 06302 15.87 8 .1285 16,610 .04998 20.01 .1144 13,090 .03963 25.23 10 .1019 10,380 .03143 31.82 11 .09074 8.234 . 02493 40.12 12 .08081 6,630 .01977 50.59 13 .07196 6,178 .01568 63.79 14 .06408 4,107 .01243 80.44 15 .05707 3,257 .009858 101.4 16 .05082 2,583 .007818 127.9 17 .04526 2,048 .006200 161.3 18 .04030 1,624 .004917 203.4 19 . 03589 1,288 .003899 256.5 20 .03196 1,022 .003092 323.4 21 .02846 810.1 .002452 407.8 22 .02535 642.4 .001946 514.2 23 .02257 509.5 .001542 648.4 24 .02010 404 .001223 817.6 25 . 01790 320.4 .0009699 1,031 28 .01594 254.1 .0007692 1,300 27 .0142 201.5 .0006100 1.639 28 .01264 159.8 .0004837 2.067 29 .01126 126.7 .0003836 2,607 30 .01003 100.5 . 0003042 2,287 31 .008928 79.7 .0002413 1,145 32 .00795 63.21 .0001913 5,227 33 .00708 60.13 .0001517 6,591 34 . 006305 39.75 .0001203 8,311 35 .005615 31.52 .00009543 10.480 36 .005 25 .00007568 13,210 37 .004453 19.83 .00006001 16.660 38 . 003965 15.72 .00004759 21,010 39 .003531 12.47 . 00003774 26,500 40 . 003145 9.888 00002993 33,410 CONDUCTORS. Copp«r-Wlpe Table — (Coniinued). 155 Resistance. Gauge. B.&S. Weight. Pounds per ohm. length. Feet per ohm. Ohms per Ohms per pound. foot. 0000 13,090 20,440 0.00007639 0.00004893 000 8.232 16,210 .0001215 .00006170 00 5,177 12,850 .0001931 .00007780 3,256 10,190 .0003071 .00009811 1 2.048 8,083 .0004883 .0001237 2 1.288 6,410 .0007765 .0001560 3 810 5,084 .001235 .0001967 4 509.4 4,031 .001963 .0002480 5 320.4 3,197 .003122 .0003128 6 201.5 2,535 .004963 .0003944 7 126.7 2,011 .007892 .0004973 8 79.69 1,595 .01255 .0006271 9 50.12 1,265 .01995 .0007908 10 31.52 1,003 .03173 .0009972 11 19.82 795.3 .05045 .001257 12 12.47 630.7 .08022 .001586 13 7.84 500.1 .1276 .001999 14 4.931 396.6 .2028 .002521 15 3.101 314.5 .3225 .003179 16 1.950 249.4 .5128 .004009 17 1.226 197.8 .8153 .005056 18 .7713 156.9 1.296 .006374 19 .4851 124.4 2.061 .008038 20 .3051 98.66 3.278 .01014 21 .1919 78.24 5.212 .01278 22 .1207 62.05 8.287 .01612 23 .07589 49.21 13.18 .02032 24 .04773 39.02 20.95 .02563 25 .03002 30.95 33.32 .03231 26 .01888 24.54 52.97 .04075 27 .01187 19.46 84.23 .05138 28 .007466 15.43 133.9 .06479 29 .004696 12.24 213 .0817 30 .002953 9.707 338.6 .103 31 .001857 7.698 538.4 .1299 32 .001168 6.105 856.2 .1638 33 .0007346 4.841 1.361 .2066 34 .0004620 3.839 2.165 .2605 35 .0002905 3.045 3,441 .3284 36 .0001827 2.414 5,473 .4142 37 0001149 1.915 8.702 .5222 38 00007210 1.519 13,870 .6585 39 .00004545 1.204 22,000 .8304 40 .00002858 0.955 34,980 1.047 The table is calculated for a temperature of 20^ C. Resistance in inters national ohms, for resistance at 0° C, multiply values in table by 0.9262; for resistance at 50° C, multiply by 1.11723, and for resistance at 80° C, multiply by 1.23815. The following data were used in computing the table: Specific gravity of copper = 8.89. Matthiessen's standard 1 meter- gram of hard drawn copper at 0** C.== 0.1469 British Association unit (B.A.U.) = 0.14493 international ohm (1 B.A.U. = 0.9866 international ohm.) Ratio of resistivity of hard to soft copper =1.0226. Temperature coefficients of resistance for 20°, 50°, and 80° C. (cool, warm, and hot) taken as 1.07968. 1.20625. and 1.33681, respectively. Aluminum Wires at 75° F. (Pittsburgh Reduction Co.). 156 ELECTBOTECHNICS. R&l*. ^l!^^"" Feet per ohm. Ohms per lb. 0000* 0*08177 12,229.8 0.00042714 000 .1031 9,699 .00067022 00 .1300 7,692 .00108116 .1639 6,245.4 .0016739 1 .2067 4,637.4 .0027272 2 .2608 3.836.2 .0043441 3 .3287 3,036.1 .0069057 4 .4145 2,412.6 .0109773 Conductivity taken as 60% of that of pure copper. Weight of pure aluminum taken as 167.111 lbs. per cu. ft. General Formulas for Wiring;. (From General Electric Co. literature.) Area of conductor in circular mUs ^'DWK-i-PE^; Volts lost in line = PEM -t-100: Current in main conductors =» TFT -t-^; Weight of copper in \ine='AWKD^-i-PEXlO^; where Z) = distance of transmission (one way) in feet, TF = total watts delivered at the end of line, P = per cent loss of W in line, and ^ = voltage between the conductors at the receiving end of line. A, K, and T are constants having the following values: K A , Per cent power factor x 100 95 90 85 80 Single-phase 6.04 2160 2400 2660 3000 3380 Two-phase (4 wires) . . 12.08 1080 1200 1330 1500 1690 Three-phase (3 wires). 9.06 1080 1200 1330 1500 1690 T , Per cent power factor s 100 95 90 85 80 Single-phase 1 1.06 1.11 1.17 1.26 Two-phase (4 wires) 0.5 .53 .66 .69 .62 Three-phase (3 wires) 68 .61 .64 .68 .72 K for continuous current — 2160, r=« 1, il = 6.04, and JW-1. Values of ilf . — Wires 18 in. apart from c. to c. Gauge : 25 Cycles. 40 Cycles. B. & S. ^Power factor in per cent.— > r-Power factor in per cent.— % 95 90 85 80 95 90 86 80 0000 1.23 1.29 1.33 1.34 1.52 1.63 1.61 1.67 000 1.18 1.22 1.24 1.24 1.40 1.41 1.48 1.61 00 1.14 1.16 1.16 1.16 1.25 1.32 1.35 1.37 1.10 1.11 1.10 1.09 1.19 1.24 1.26 1.26 1 1.07 1.07 1.05 1.03 1.14 1.17 1.18 1.17 2 1.06 1.04 1.02 1.00 1.11 1.12 1.12 1.10 3 1.03 1.02 1.00 1.07 1.08 1.07 1.05 4 1.02 1.00 1.06 1.06 1.03 1.00 6 1.00 1.03 1.01 1.00 6 1.02 1.00 7 1.01 8 1.00 60 CJydes. 125 Cycles. r-Power factor in per cent.— » —Power factor in per cent.-^ 96 90 85 80 96 90 85 80 0000 1.62 1.84 1.99 2.09 2.36 2.86 3.24 3.49 000 1.49 1.66 1.77 1.95 2.08 2.48 2.77 2.94 00 1.34 1.62 1.60 1.66 1.86 2.18 2.40 2.57 1.31 1.40 1.46 1.49 • 1.71 1.96 2.13 2.26 1 1.24 1.30 1.34 1.36 1.66 1.76 1.88 1.97 2 1.18 1.23 1.25 1.26 1.45 1.60 1.70 1.77 3 1.14 1.17 1.18 1.17 1.35 1.46 1.53 1.57 4 1.11 1.12 1.11 1.10 1.27 1.36 1.40 1.43 6 1.08 1.08 1.06 1.04 1.21 1.27 1.30 1.31 6 1.06 1.04 1.02 1.00 1.16 1.20 1.21 1.21 7 1.03 1.02 1.00 1.12 1.14 1.14 1.13 8 1.02 1.00 1.09 1.10 1.09 1.07 9 1.00 1.06 1.06 1.04 1.02 10 1.04 1.03 1.00 1.00 The values of M in the above table are about true for 10% line loss. CONDUCTORS. 157 They are reasonably accurate for losses less than 10%, under 40 cycles, and close enough for larger losses. If the largest conductors are used at 125 cycles and the loss is greater than 20%, the values should not be used. If the conductors are closer to each other than 18 inches, the loss will be less than that given by the formula, and if very close together, as in a cable, the loss will be that due to resistance only. For a direct -current 3-wire sjrsteni, the neutral feeder should have a section equal to one-third of that of the outside wires as obtained from formula. For both alternating and direct current the secondary mains and the house wiring should have the neutral wire of the same area as the outside conductors. For the monocyclic system (power and lights) calculate the primary circuit as if all tne power were transmitted over the outside wires, the size of the power wire to be to either outside wire as the motor load (in amperes) is to the total load in amperes. Secondaries leading to induction motors should all be of the same size as for a single-phase cireuit of the same capacity in kilowatts and same power factor. The three lines of a 3-phase circuit should be of equal cross-section. Power Factor: — When not more accurately determinable, take as follows: Lighting only? 95% ; lighting and motors, 85% ; motors only, 80%. For lighting circuits using small transformers the voltage at transformer primaries should be 3% higher than the voltage X ratio of transformation. For motor circuits substitute 6% for 3% in the preceding rule. Examples: — Direct-current circuit, 1,000 110- volt lamps, each taking 0.5 ampere; line loss, 10%; two wires: distance, 2,000 feet. arcularmil8-2,160X2,OOOX(l,OOOX0.5X110) + (10X1102) = l,963,636. Volts drop to lamps = 10X110X1-4- 100 =11 volts. Three- wire circuit, — 220 volts between the outside wires: Area of each outside conductor = 2,160 X 2,000 X ( 1 ,000 X 0.5 X 1 10) -^ (10 X 220*) «= 490,- 900 cir. mils. Area of neutral or third wire = 490,900 -5- 3 = 163,633 cir. mils. Volts loss in circuit = 10 X 220 X 1 -^ 100 = 22 volts. Alternating currents: Two- wire, single-phase; 10 to 1 transformers 2 volts loss in secondary wiring; transformer drop = 3%; loss in primary line to be 5% of the delivered power; efficiency of traAsformer = 97%. Volts at transformer primaries = (110 -1-2) X 10X1.03 = 1153.6. Watts required by lamps= 1,000X110X0.5 = 55,000. Watts required at primaries = 65,000 -t- (0.98X0.97) = 58,000. Qr. mils = 2,000 X 58,000 X 2,400 -i- (5 X 1 .153.62) = 41 ,760. Three-phase, 3- wire power transmission, 60 cycles; 3,500 H.P., 6 miles; loss, 10% of delivered power; voltage at motor — 5,000; power factor of load = 85%. arcular mils « (5,280 X 5) X (3,500 X 746) X 1,500-*- (10X5,0002) = 413,582. Two 0000 wires have this area, also four wires. If the latter are used, the drop will be only 73.3% of that when using the larger wires (j^) • Per cent loss = 5,280 X5X 3,500 X 746 X 1500 + (4 X 105,592) X 5.0002=9.79% of the delivered power, or 322.6 H.P. loss in the transmission. Volts lost in line = 9.79X5,000 XI. 46 -1-100 = 715. Volts at generator = 5,000 -I- 715 = 5,715. Current in line = 3,500 X 746 X 0.68-1-5,000 = 355 amperes. Calculations applying to Transmission Circuits. The E.M.F.'s in the various parts of a transmission system may be calculated by means of the following table and the method employed in the example given. Line Constants. (Wires 18 in. apart.) Gauge, Wt.,Diam. Area, , Reactance, X, . B.&S. lbs. mils. cir. mils. R. L. C. i. /=25 40 60 125. 0000 3,376 460 211,600 .266 1.48 .0102 .0385 .232 .372 .558 1.16 000 2,677 410 167,800 .335 1.52 .00996 .0375 .239 .382 .573 1.19 00 2,123 365 133,100 .422 1.56 .00973 .0366 .245 .392 .588 1.22 1,685 325 105,500 .533 1.60 .00949 .0358 .251 .402 .603 1.26 1 1335 289 83,690 .671 1.63 .00926 .0349 .256 .409 .614 1.28- 2 1,059 258 66,370 .845 1.66 .00909 .0342 .261 .417 .625 1.30 3 840 229 52.630 1.067 1.70 .00883 .0333 .267 .427 .641 1.33 4 666 204 41,740 1.346 1.73 .00^63 .0326 .272 .435 .652 1.36 5 528 182 33,100 1.700 1.77 .00845 .0319 .278 .445 .667 1.39 6 419 162 26.250 2.138 1.81 .00827 .0312 .284 .455 .682 1.42 7 332 144 20,820 2.698 1.84 .00809 .0305 .289 .462 .693 1.44 8 263 128 16,510 3.406 1.88 .00793 .0295 .295 .472 .708 1.48 158 ELECTROTECHNICS. Weight given in lbs', per mile of wire; R^^ohms per mile of conductor : Zr —inductance in millihenrys per mile; C = capacity in microfarads, of two wires, each one mile in length; t = charging current of line of two wires (/-60, ^ =10,000 volts) -2.t/CJE:10-6; X- reactance «2;r/L10-3. Impedance, Z = Vfl2+X2. Let it be required to transmit 2,700 H.P. over a S-phase circuit 10 miles in length, the power being generated at 1,000 volts, raised through a step- up transformer to 10,000 volts for transmission along the line, and reduced to 1,000 volts at the receiving end by a step-down transformer. IVans- former efficiencies =07.5%; copper loss in each, 1%; core or hysteresis loss, in each, 1.5%; reactance =3.59^; magnetizing current = 4%. Loss intransmission*-15%, lOof which isinhne; power factor*- 0.85. Voltage between any branch and the common center of system =^-^V^^ 10.000 + v^3 = 5,774. Energy delivered by each wire -2,700X746 -5-3 = 671,400 watts. Apparent energy per branch -67 1,400-*- 0.85 -790,000 watts. Current in each wire — 790,000 -^ 5,774 — 136.8 amperes. Drop in each wire— 10% of 5,774-577.4 volts. Resistance of each wire = 577.4 -s- 136.8 — 4.22 ohms, or 0.422 ohms per mile, which is the resistance of a 00 wire; consequently, three 00 wires will carry the load# Reactance of 10 miles single conductor— 0.588X10 — 5.88 ohms. Inductance for 10 miles — 10X1.56 — 15.6 millihenrys. Charging current for each line, for 10 miles - .0 366X10- 0.366 amp. Power factor being 0.85, the induct- ance factor- >/l -0.852-0.52. To find the E.M.F. at generator and the distribution of current when fuU load is on, the entire system may be considered at 10,000 volts for convenience in calculation. Impressed E.M.F. - ^2 (energy EM.F.'a)^+I (Induction E.M.F. 's)2. Commencing with the secondary circuit, working back and tabulating the steps, the following is obtained: EjS'I^ '"l"l§^r Current. Secondary Circuit ; Energy, E.M.F. -5.774X0.85 -4,909 Inductive E.M.F. - 5,774 X 0.52 - 3,003 Current, in amperes — 136.8 Step-down Transformers : ResiBtanoe loss, /A-1% of 5,774 - 58 Reactance " /JT- 3.5% of 5,774 - 202 Hysteresis ** -1.5% of 136.8 - 2.05 4.967 3,205 138.85 Line* Resistance loss, 7/2-138.85X4.22 - 686 Reactance " ZX - 138.85 X 5.88 - 817 5,553 4,022 138.85 (Volts at te rminals of step- up trans- formers - ^5 .5532 -f 4 ,0222 - 6 ,857. ) Step-up Transformers: Resistance loss, 7/2 — 1% of 6.857 — 69 Reactance " 7X- 3.5% of 6.857 - 240 Hysteresis *' 1.5% of 138.85 =» 2.08 5,622 4,262 140.93 Volts at generator - ^5^622^ + 4 ,2622 == 7 ^065 volts, or, reduced by 10. 1 ratio, —705.5 volts, lor one branch. The total generator E.M.F. would then be 705.5 X >/3~= 1,21^ volts, or total volts at generator = 122.2% of volts at secondaries of receiving transformers, and the power factor of the entire circuit is 1,000-5-1.222 = 0.818. Inductance for Parallel Copper Wires, Insulated. L per 1,000 feet per wire = 0.01 524 -I- 0.1 4 log — ; /. per 1,000 ft. of the whole circuit for a CONDUCTORS. 159 3-phase line— 0.02639+0.2425 log —, where L is in millihenrys, d and r being respectively the distance between centers of wires and radius of wire, both measured with the same unit. Capacities of Conductors. Jx^ad-prutected cables: Microfarads per 1,000 ft. of length '=0.007361iiC -flog — . Single overhead conductors, with earth return: Microfarads per 1,000 ft. =0.007361+ log -r. Each of two parallel, bare aerial wires: Microfarads per 1,000 ft.« 0.003681 -5- log—. In the above, /) = diam. of cable outside of insulation, d = diam. of conductor, di = distance between wires, c. to c, A = height above ground, r«^ radius of wire, /C— specific inductive capacity of in- sulating material. D, d, di, h, and r should all be measured by the same unit. Heating of Conductors. Jn&ulated parallel wires: Diam. in inches == 0.01 47^^ (Kennelly). Bare T*ires: Diam. in mils = 45 v /2+ (T~t\ where /= current in amperes, r = temp. of wire, and <=temp. of air, both in degs. F. Carrying Capacity of Interior Wires and Cables (A. I. E. £.). B.&S. Rubber- Weather- Circular Rubber- Weather- Gaup. covered. proof. mils. covered. proof. 12 16 400.000 330 500 12 17 23 600,000 450 680 10 24 32 800.000 550 840 8 33 46 1,000,000 650 1000 6 46 65 1,500.000 850 1360 4 66 92 2.000,000 1050 1670 2 90 131 The capacities are in am- 127 185 peres. No smaller wire 000 177 262 than No. 14 to be used. 0000 210 312 Rubber covering to be A i". thick for No. 14 to No. 8. A in. for No. 7 to No. 2. A in. for No. I to 0000. A in. for No. 0000 to 500,000 cir. mUs., A in. up to 1,000,000 cir. mils, and i in. above 1,000,000 cir. mils. Weather- groof coverings must have the same thicknesses, the inner coating to be reproof and 0.6 of the total thickness. Insulation Resistance (National Code). The wiring in complete instal- . , ,. . , / 20,000.000 \ . ^ lations must have an msulation resistance = ( -— 5 — : — 1 m ohms. vamperes nowmg / Fuses. Fuses for 5 amperes and less should be 1.5 in. long, and 0.5 in. should be added for each additional 5 amperes. Round wire should not be ufied for over 30 amp., — above that, use a flat strip. Fusing current — a^, where d»diam. in inches and. a is a constant having the following values: copper, 10,244; aluminum, 7,585; platinum, 5,172; iron, 3,148; tin. 1,642; lead, 1,379; 2 lead + 1 tin, 1,318. Diameter in Inches. nperes. Copper. Iron. Tin. Lead. 1 10 50 100 200 300 .0021 .0098 .0288 .0457 .0725 .095 .0047 .0216 .0632 .1003 .1592 .2086 .0072 .0334 .0975 .1548 .2457 .322 .0081 .0375 .1095 .1739 .276 .3617 (Preece.) ELECTRIC LIGHTING. Arc Lamps. 45 to 60 volts, 9.6 to 10 amp., 2,000 candle-power (nomi- nal); 45 to 50 volts, 6.8 amp., 1,200 candle-power (nominal). Enclosed arcs require 80 volts, 5 amperes; carbons burn front 100 to 150 hours. Alternating-current arc lamps require 28 to 30 volts and 15 amperes. 160 ELECTROTECHNICS. The mean spherical candle-power (c.-p.) is the mean of that over a sphere of which the light is the center and equals, approximately, "o" "^"'T » where // is the horizontal c.-p. and M the maxinmni c.-p. (40** b«low hori- zontal for a direct-current arc). The continental unit of light is the hefner. or 0.88 candle-power. Ciear-glas5 globes cut off 10% of the illumination, ground-glass globes from 35 to 50%, and opal globes from 50 to 60%. Incandescent Lamps, usually 16 c.-p., require from 3 to 3.5 watts per c.-p. and have a life of 800 to 1,000 hours. They f>hould not, however, be used over 600 hours, as their efficiencies decrease during use. The most economical point at which to renew a lamp (i.e. the "snaaahing" point) may be found as follows: : Hours lamp should be used—cV^T^, where 5 = cost of lamp per c.-p., JE!— cost of 1,000 \^att-hours of energy, and c = 1,410 when the increase of watts per c.-p. per hour of use =0.001 (c = l,0()0 when increase »0.002, and 815 when increase =0.003). The Tantalum Incandescent Lamp has a fine wire of this rare metal in place of the ordinary carbon filament. Properties of tantalum : melting pomt =2,300° C, sp. heat =0.0365 ; sp. g. = 16.5 : sp. resistance (Im. X Imm.*) =0.165 ohm. The resisti\'ity increase? with the temperature and at 1.5 watts per c.-p. =0.855. Lamps (1.5 watts per c.-p.) have a useful life of 400 to 600 hours. niumlnation. Arc lamps: for outdoor or street illumination, 100 to 150 sq. ft. per watt; for railway stations, 10 to 18 sq. ft. per watt; for large halls, exhibitions, etc, 2 sq. ft. per watt; for reading-rooms, 1 sq. ft. per watt and for intense illumination 0.5 sq. ft. per watt. Incandescent lamps: (16 c.-p.). Ordinary illumination, sheds, depots, etc., 1 lamp (8 ft. from floor) for 100 sq. ft.; waiting-rooms, 1 lamp for 75 sq. ft. ; stores and offices, 1 lamp for 60 sq. ft. Dark walls require an increase in the above figures. Nernst lamps, having a "glower" formed of metallic oxides which becomes incandescent during the passage of current, are made in sizes from 25 to 150 c.-p. and require about 1.6 watts per c.-p. ELECTRIC TBACTION. Tractive Force and Power. The force, F, required to bring a car from rest to a certain speed, «, (in miles per hour,) within a given time. 91 \W% t, (in seconds,) is F (in lbs.) — /H — b20Wp, where W' = weight of car in tons, / = (20 to 30)XTT'', and p = per cent of grade. It takes a pull of about 70 lbs. per ton to start a car on a level or to round a curve. If there is a grade, the starting pull in lbs. = (70-l-20p)Tr, ba.«^d on a speed of 9 miles per hour being attained in 20 sees. The average II.P. required = 0.00133F«-i-ij, where iy = efficiency of motor (from 50 to 60%). The per cent grade, p, at which slipping occurs when car is starting = ^ — 3.6, where o = ratio of adhesive force to weight on X drivers, =0.125 to 0.16. and x = weight on drivers -s- total weight of cor. When runmng, p = 1.5. X Resistance of Rails used for Returns. Cir. mils of cross-sectioi* of a rail = 1 24,750 TT; equivalent cir. mils of rail section in copper = 20 ,800 TT; Resistance of a single rail per mile in ohms = 2.5-5- TT. approx. (Varies from 2.5 to 5 according to the chemical composition of rail.) IF = weight of rail in lbs. per yard. Safe Current for Feeders, in amperes, = v^(diam. in mils )3-i- 1,300. Heavy Electric Railroading. Train resistance, R, in lbs. per ton of 2,000 lbs. = 3 -I- 1.678 4- 0.0025 , where » = speed in miles per hour, w i4= cross-section of car in sq. ft., tf? = weight of train in tons of 2.000 \h». This formula was found aDr>lifable to conditions met with on the Long Island Ry. (W. N. Smith, A. I. E. E., 11-25, 1904). ELECTRIC TRACTION. 161 A formula due to Aspinall is said to give satisfactory results: R (in lbs. per metric ton of 2,200 lbs.)='2.5+«5 + (5I +0.028L), where Z/ = length of train in feet. The starting resistance varies according to the wheel diameter, condition of track, etc. Aspinall gives as a fair average 17 ibs. per ton of 2.200 lb.-<. for best conditions. Electric Passenger Locomotive (N.Y.C. & H.U.Ry.). Type 2-8-2; drivers 44 in. diam.; trucks, 36 in. diam. *. diam. of driving axles = 8.5 in.; wheel-base of drivers = 1 5 ft., total wheel-base = 27 ft. Weight on drivers — 138,000 lbs.; on trucks, 52,00ri lbs.; total weight -190,000 lbs. Power; direct current, 600 volts; 4 motors, each 550 rated II. I*. Max- imum power=3,000 H.P. Normal full-load current = 3,050 amperes. Max. current = 4,300 amp. Normal draw-bar pull » 20,400 lbs., max pull = 32,000 lbs. Speed with a 500-ton train = 60 miles per hour. (General Electric Co., builders.) ADDENDA. I^arfjj^ Gas En^nes. Bel^an and German Practice. Compression, 170 to 200 lbs. per sq. in. ; m.e.p. generally taken as 70 lbs. per sq. in. CooUng- water per B.H.P. per hour: cyhnders, cylinder-ends and stuffing- boxes, 4 to 5.25 gal.; pistons and piston-rods (hollow), 1.75 to 2.75 gal.; valve-boxes, seats and exhaust- valves, 0.88 to 1.38 gal. (Water entering at 60° F. and leaving at 95** to 115° F.) Engines are started by com- pressed air (150 to 250 lbs. per sq. in.) and the lubrication is effected by means of a forced oil-feed. The foregoing for engines of 200 to 1,000 H.P. An Otto-Deutz 4-cycle, double-acting en^ne (223 B.H.P.) using suction- producer gas made from Belgian anthracite (14,650 B.T.U. per lb.) re- quired 0.704 lb. of dry coal per B.H.P. hour. (R. E. Mathot, Liege Meet- ing of I. M. E., 1905.) Shearinfir Streng^th of Rivets in IIm. per sq. in. Single-shear: Iron, 40,000: steel, 49,000. Double-shear: Iron, 78,000; steel, 84,000. Dis- tance from center of rivet hole to edge of plate should be about 2d. (E. 8. Fitzsimmons, Master Steam-Boiler Makers' Convention, 1905.) A safety factor of 4^ should be employed. In butt-joints with two butt-straps or cover plates the rivets are in double shear (page 21). Flow of Air in Metal Pipes. Q = ct -v— , where d=side or diam. in in., F = friction in ounces per sq. in., L = length in ft., Q = cu. ft. per min., C — 4A for roimd and 5.5 for square pipes. For a 90° bend in the pipe, add E feet to L. (E='kd.) Let r=mean radius of bend in in. Then, when r-«-d = 0.5 1 1.5 2 k = 5' 4 3 2 (J. H. Kinealy, E. N., Aug. 10, 1905.) When r = 2.5 d the bend oflFers the least resistance, and E (in inches )=» 3.38 X length of the ciirved portion of pipe, measured along the center line at radius r. (C. W. L. Alexander, Trans. I. C. E., 1905.) APPENDIX. MATHEMATICS. Metric H.P. (Force de cheval). 1 metric H.P. = 75 m.-kgs. per sec." 642.475 ft.-lbs. per sec. = 0.9863 British H.P. (1 British H.P. = 1.01389 metric H.P.). 1 meter-kilogram (m.-kg.) =7.233 ft.-lbs. 1 ft.-lb = 0.138265 m.-kg. Galdinus* Theorems for Areas and Volumes. 1 . If a straight or curved line in a plane revolves about an axis Ijdng in that plane, the area of the surface so generated is egual to the length of the hne multiplied by the distance through which its center of gravity moves. 2. If a plane ar^a revolves about an external axis in the same plane, the volume of the solid so generated is equal to the area of the figure mul- tiplied by the distance through which its center of gravity moves. Centers of Gravity of Lines. Straight line: Its middle point. Circumference of a triangle: Form an inner triangle bv connecting middle points of sides and inscribe a circle; the center of circle is c. of g. desired. Circumference of parallelogram: At intersection of diagonals. Circular arc: On middle radius at distance x from center of circle [x = (chord X ra- dius) -s- length of arc]. For very flat arcs c. pf g. lies ih from chord, where ^-height of arc. MATBRIAI^S. Metals, Properties of. g p Lbs. per Fusing- °^' ^' cu. m points. Antimony 6.7 0.242 806° F. Bismuth.... 9.8 .354 516 Lead 11.38 .411 620 Manganese 8. 289 3,452 Nickel 9. .325 2,678 Platinum 21 .6 ^76 3,272 \11oys. Sterro Metal (Tensile strength r.S.=» 60,000 lbs. per sq ia.): 55% Cu + 42.36% Zn + 1.77% Fe + 0.1% Sn + 0.83% P. TFolfram- Jnlum: 0.375% Cu+0.105% Sn + 98.04% Al + 1.442% Sb + 0.038 W. illasnalium: 2 to 25% Mg + 98 to 75% Al. Sp.g., 2.4 to 2.54; fuaing- point, 1,100* to 1,300° F. With 10% Mg, alloy has properties of rolled zinc; with 25%, those of bronze. Parsons' Manganese Bronze : 60% Cu + 37.5% Zn + 1.5% Fe + 0.75 %Sn + 0.01% Mn + 0.01% Pb (for sheets): 56% Cu + 42.4% Zn + 1.25% Fe+0.75% Sn + 0.6% AH-0.12% Mn (for sand castings). T.S. = 70,000 lbs. per sq. in.; elastic limit, 30,000 lbs.; elongation in 6 in. = 18%; reduction of area = 26%. Niclcel- Vanadium Steel. (Carbon content = 0.2%.) With 2% Ni, and 0.7% V, tensile strength = 90,000 lbs. per sq. in; increasing V to 1%, T.S.- 120,000. With 12% Ni and 0.7% V, T.S. « 200,000; increasing V 162 APPENDIX. 163 to 1%. T.S.» 220,000. By temperinff the 90.000 lb. steel (heatinf to 1^60* F. and quenching in water at 68*' F.) its T.S. is raised to 168,000. ElsBtic limits about 80% of T.S. Elongation for 2% Ni steels about 22%; for 12% Ni = 6%. Halleable Iron, Ultimate Strength. Round bars tensile strength — 43,000 lbs. per sq. in., approx.; elongation = 7% in 8 in.; reduction of area = 3.75%. Square and star-shaped sections have about 85% of the strength of circiilar sections. Compressive strength is from 31,000 to 34,000 lbs. per sq. in. (Mason and Day.) Steel. Each per cent, of the carbon content of a steel is divided into 100 parts, each of which is called a "point"; thus, a 40-point carbon steel is one containing 0.4% of carbon, Portland Cement Concrete in Compression ('safe strength). /« (di- rect compression) = 4,260-*- («+fli+ 4.4), where s ana g are the No. of parts of sand and gravel in the mixture to one part of cement (c). For one cubic yard of concrete, No of bbls. of cement, N = ll-i-{c+8+g): No. cu. yds. sand=>0.141i\r«; No. cu. yds. gravel or crushed stone -=0.1 41 iV^. (1 bhl.— 3.8 cu. ft.) STRENGTH OF MATEBIALS. Elastic Limit. Yield-Point. Permanent Set. The elastic limit is the point at which the strains begin to increase more rapidly than the stresses causing them. This increase of strain is initially slight but becomes marked later at what is called the "yield-point" (e.g., ndien scale-beam of a testing machine suddenly drops). That part of the strain which does not disappear when the stress is removed is called . the "permanent set." If none of the strain disappears on removal of the stress, the material is said to be "plastic," if the greater part remains, the material is "ductile," and *f the material breaks under very low stress and slight stretch, it is said to be "brittle." Transverse Elasticity (see page 18). In formula C— /a+^ai ^s is the strain between two shear planes 1 in. apart. Pure Shear Stress (Ultimate) =CXult. tensile stress, where C— 1.2 (1.1 to 1.5) for C. I., 1.25 for phosohor bronze and yellow brass, 0.9 for gun-metal, 0.6 for alloy bronzes, 0.75 lor W. I., and 0.12 carbon steel, and 0.65 for 0.70 carbon steel. (E. G. Izod, Engineer, London. 12-29-'06.) Aluminum (99% pure). Breaking and safe stresses in lbs. per sq. in.: Tension. Compression. Breaking. Safe. Breaking. Safe. Castings 14,000-18,000 3,500-4,500 16,000 3.000 Sheets, bars 25,000-40,000 6,000-7,000 20,000 5,000 Wire 30,000-35,000 (^-11,500,000 for cast metal.) Allowable Fiber Stresses in Lbs. per Sq. In. (Bach W. I. Steel. C. I. Low High Cast- Carbon. Carbon. ings. Tension,/*- 12,800 12.800 17,000 8,500 4.300 17,000 21,300 12.800 Compression,/*- 12,800 ** ** 12,800 12,800 17,000 Bending, /&- *• •• " 10,700 (a) 15.000 Shearing, /«- 10,200 10,200 13,700 6,800 4,300 13,700 17.000 12,000 Torsion, /ew- 6,100 8,500 12,800 (6) 12,000 17 000 (The higher values are for homogeneous metal, not too soft.) (o) For rect. sections, 7,300; circular, 8,800; I sections, 6,200. lb) For circ. sections, solid and hollow, 4,3()0; eUiptic and hollow rect.. APPENDIX. ) to 5,300; rect., square, I, channel, an^e, and cruciform sections, ) to 8,000. e values above given are for constant stresses due to a dead load, P. r repeated stresses: (1) load fluctuating between and +P, take f of tabular values; (2) *• " •• +P •• -P. •• i r spring steel (1), f6 = 52,000 (untiardened) or 62,000 f hardened). renfirth of Cylinders. According to Prof. C. H. Benjamin, if the es of a C. I. cylinder are unsupported, the initial fracture will be cir- erential, near the flanges, and will be caused by a pressure much ihan p = 2ft-i-d. Also, if flanges are sufficiently braced oy brackets to e longitudinal fracture, a considerable allowance (say i) must be 5 for bending and other accidental stresses. Hydraulic cylinders r pressures above 3,000 lbs. should be made from air-furnace iron or castings, as water will ooze through ordinary, open-grain C. I. walls in. thick. (A. Falkenau, Am. Mach., 1-4-06.) e thickness, t, of the walls of a cylinder under internal pressure, p, be found from the following formula, which is a simplification by the )T of a rather unwieldy one due to C. Bach: <=0.42pd-J-(/« — 1>), where iam, of cylinder and /««= allowable stress in the material employed (to ed only when j)<0.77/f), lues of //: C. I. and bronze, 4,300 to 8,500 (and even 10,000 for strong ; phosphor-bronze, 7,100 to 14,200; cast steel, 14,200 to 17,000 (for lesmann tubes of Martin steel, 18,000 to 43,000); W. I., 12,800 to 0. t and d in in., p and ft in lbs. per sq. in. tter Joints (W. I. and Machinery Steel). Diam. of rod, d, is en- i to D( = 1.33rf) in socket. Socket diam. = 2Z) = 2.66d; thickness of iiteel) =0.25D; mid-depth of key, A = 1 .33D = 1 .75<i. Ends of socket od should extend fh to fh beyond key slots ( = 1.25d, average). r-Wheels, Safe Velocities for. Velocity in ft. per sec.^ '^STjft-i-w, where « = factor of safety, ij = efficiency of joint used, to— f 1 cu. in. of material, and /(» tensile stress of material. Hard Cast rx-_i Maple. Iron. ^*®®*- w = .0283 .261 .283 ft - 10,500 10,000 60,000 « = 40 10 20 wooden rims «»20, but as the segments break joints in assembling rength is reduced one-half, making s really equal to 40. Steel rims are up from segments riveted together, and the usual factor 10 issimi- increased to 20. Using above values and considering wheels as ij = l. For cast-iron rims, ij = 0.25 for flange-joints between arms, for pad-joints (each arm having a flat enlarged face on its end to I rim-sections are bolted), = 0.6 in heavy, thick-rimmed balance-wheels joints reinforced by steel links which are shrunk on. (W. H. Boehm, mrance Engineering.) ireted Joints. General Formulas. (W. M. Barnard.) ciency of joint = 1 -^[1 +ff^(nff+mf/)]. ,he above n = No. of rivets in single shear in a unit strip equal to the pitch (where rows have different pitches), and w — No. of rivets simi- in double shear. / and /' are respectively strengths in single and e shear. Ton) varies from 40,000 for single-riveting, punched holes to 50,000 juble-riveting, drilled holes, fi (steel) = 55,000 (punched holes) to ) (drilled holes). /« (iron) = 36,000 to 40,000; fa (steel) = 45,000 to ). ron) =67,000 (for lap-joint) and 90,000 (for butt-joint); fc (steel) — ) (lap) and 100,000 (butt). Ileal Springs of Phosi)hor-Bronze will withstand the action of ater. For wire up to f in. diam. use formulas on pages 23 and 24. I fa = 17.825, and C = 6,200,000. (H. R. Gilson, Am. Mach., 7-19-'06.) APPENDIX. 165 Moment of Inertia. The following graphic method is in extended use among designers of structural steel. Divide area of section A (Fig. 38) into 10 or more strips parallel to direction of neutral axis desired, and set off lengths reprfsenting their respective areas on the polar diagram at the left, as 01, 12, 23, . . tnn. These strip areas are to be considered as parallel forces which act at their respective centers of gravity as indicated by the small circles. Set off pole O, making OB'^^A, and draw OO, 01, 02, ... On. Draw iiC0||O0. OljIOl, 121)02. .... closmg diagram witn nL\\On. At /, the intersection of nil and AO, draw JX^ which is the neutral axis of the section. Find the Fig. 38. area of the equilibrium polygon, Ai, then, Moment of Inertia of Section » area AX area Ai. (The greater the number of strips, the more accurate the results obtained.) LAminated Sprin^^s. For nearly flat springs, Deflection J = WP-*- 4,460n6t' (approx.), but for exact results, as true for buffing as for ordi- nary springs, Deflection — J[l —c(6c — 7i) + 3i2]-5-3P, where Z = length of arc of top plate, c= camber, b and < = width and thickness (all in inches), n»No. of plates, and TF=load in tons. (H. E. Wimperis, Engineer, Lon- don. 9-15- '05.) Strength of Forced Bings (for hoisting, etc.). Consider the sus- pended ring to be divided into two equal parts by a vert, plane, i of total load Wi acting on each half. Employ formula for combined tension and bending (page 29): /t = ^(^+^)' ^^^re 1^-^\ a = ;r(P^4, r = 0.5(D4-rf), where D = internal diam. of ring and <f = diam. of iron used, c = 1.6 for W. I. or steel, « = jrd»-5-32. This reduces to: ftcP-2.23Wxd=l.6W D, in which /« = 5,000 to 6,000 lbs. per sq. in. for safe tensile stress (allowing for sud- denly applied load and efficiency of weld). W^ in lbs., d and D in in., any two of which being assumed, the third may be derived from formula. A formula discussed in Engineering (Ix>ndon), 5-29 '95, an<l arrived at through a different method, is: Ad«- 1 .62TF.rf- 1 62ir,D. Columns. Euler's Formulas. Safe load W =ci:^EI-i-8p, where c— 0.25 for one fixed and one free end, = 1 for both ends free, load guided, =2 166 APPENDIX S: for one fixed end and one free end, with load guided, —4 for both ends fixed, load guided: «=8afeity factor = 5 to 6 for W. I. and steel, 8 or more for C. I., and 10 for fir. The above formula should not be used where I '= length in in.) is less than 25d for W. I. and steel, or less than I2d for J, I. and wood, where d= diameter or smaller rectangular dimension of cross-section in in. For reinforoed-concrete columns, c = l, » = 10, and E=(a+ b)Ee -*- (a + 1 ) , where £e» modulus for concrete, a = concrete cross-sections steel cross- section, b — ^rtBJ •+■ ^e. For shorterbars subjected to thrust, the following formula, due to Grashof, should be employed: T-max. load in Ibs.-dfca/-*- (~+c/), where a — sectional area of bar in sq. in.; X;« 12,000 for steel ( = 10,000 for W. I.); C = 5,000 for steel and 5,600 for W. I.; c=l for bar free at both ends (e.g., connecting-rod), = 4 for bar fixed at both ends. For connecting- rods take but 75% of the above values for k. Collapse of Tubes. (Lap-welded Bessemer steel, 3 t o 10 in. in diam.) Collapsing pressure p, in lbs. per sq. in.=-l,O00(l -"^1 -(l,60(X2+rf2), where (< + d)< 0.023; p=(86,670<+d)- 1,386, where «-s-rf)> 0.023. (Ap- prox., p- 60,21 0,000«-t-d)« when («-»-d)< 0.023.) These formulas apply when l>fid. A safety factor of from 3 to 6 should be introduced, its size being according to the risk at stake to life and property. (R. T. Stewart, A. S. M. £., May. '06.) Fio. 39. Torsion and Bending (see also page 31). Accordin g to Bach, Equiv- alent Bending Moment =0.36Bm + 0.66V^J3m*+(arm)^ where a = 1.9 for W. I., 1.15 for soft steel, and 1 for hard steel. Cranked Shafts. Let abcedf (Fig. 39) be a horizontal cranked shaft. The turning force P (having a moment M, due to wt. of fly-wheel at a and equal to Pr) acts at center (e) of crank-pin in the direction indicated. Weight of fly-wheel (_W) acts vertically downward at o. Neglecting end thrust: Bearing reaction at center b (upward) — Pi ™ — , , , — ~ — . . . ; / (downward) -P.-^.+j^. Bending and Twisting Moments: at b, Bm'=Wg, Tm = Pr; at c, Bih^ Tr(m + tf)-PiW, Tm=-Pr\ at rf, Bm-^Ptn, Tm = 0; at c, Bm^P2k, Tm = Pf; at X (any point on throw) the moments Pex and pQ'fx are eacli to be resolved into- moments in and also perpendicular to the orosa-sectlon and then combined. The component in the plane of cross-dection giv«.8 Tm and APPENDIX 167 the component perp. to crossHsection gives Bm. Similarly for any point y P should also be assumed as acting downward and above values worked out for that direction. Gap Frames for BlTeters, Punches, Shears, etc. The siie and character of the work determine the depth of throat /, or distance from point of application of force w to the nearer or tension flange of frame. Assume the main section of frame (lying in a plane ± to direc- tion of force w) to be of an I-, or equivalent box-section, of area a, and having a uniform tensile stress — (due to w) distributed over it. Deter- mine position of the neutral axis of section and also its moment of inertia, /. The bending moment Bm (due to w) on the aecHowwl^^wU+x), where a; == distance from neut. axis to outer fibers of the tension nange. Tensile stress due to Bm^Bm^-*-!^ and total stress in tension flange » ^-hH a). Similarly, stress in compression flange due to Bm—-^* where y-^dist. from neut. axis to outer fibers of compression flange. This stress is opposed by the uniformly distributed tensile stress, — , and a the net stress in compression flange « , (2) . i a If (1) and (2) differ from the safe stresses for the material employed (G. I., or cast steel) the area and proportions of section must be altered until substantial agreement is arrived at. Sections parallel to direction of force w are calculated for bending only, there being no direct stress \^) on them, but the webs must have sufficient surplus section to resist shear. Steel Chimneys (self-supporting). ^» height; D and Z)i« outside and inside diams . ; T =» thickness [ = 0.5 (D — JDi)] ; Dh^ diam .of bell-fihaped baae (»I.5/> to 2/»: ^-'height of base {"Dh). All dimensions in feet. Wind pressure P (Jos. per sq. ft.) = (velocity m miles per hour)2-i-200. P is generally taken at 50 lbs., or 25 lbs. cLctual pressure per sq. ft. of pro- jected area (HD). To this is added 5 lbs. to allow for compression on one Bide, making Pg,«,=30. Bending moment, £m-=30HDX0.6H»=15/>^2. Section modulus, 5 = ^ (51^1^) = 0.78541)2^. F(per sq. ft .) = 5m + 5 =- 19.\H^-^DT, or /(sq. m.)=Q.\Z2QH^-i-DT. For steel plates /- 45,000 to 50,000, or taking strength of riveted joint as 36,000 and safety factor of 4, /,,i^9,000. To find T at any section, measure H from top of chimney to section and substitute in formula. Total wind pressure Pi = 2bHD lbs., or, if H and D are expressed in inches, Pi = 0.1736M lbs. Resistance to breaking at foundation = 1 .57db2^ -i-hf where dbt U and h are inch equivalents of Db, T, and H. For stability, make Df {pi foundation) ^g/^ -g qq^ -HO. Moment of wind pressure -=P,^(0.5jfir -J- H/'). Let 1F = total weight of chimney, lining, and foundation, m lbs.; then, x, or the lever-arm of W, '='Pi(0.5H + Hf)-i-W. If x<0.5Z)/, the structure will be stable. (0.5iV+x = factor of stability, usually about 1.6, but increased to 2.5 and even 3 for loose soil.) t should never be taken less than i to A in-, to insure durability, rivet diam., dr. not less than i in., spaced about 2.5dr (c. to c), and in any case <l(k. (1 cu. ft. of foundation weighs 125 to 150 lbs ) Foundation bolts (usually 6 or 12): Gross overturning moment *- 12.5DbH^', moment resisting overturning = 0.5T7iI>b (where TTi— wt. of shell), and net overturning moment r = 0.5Db(25H''-IF,). If Dc'=diam. of bolt circle, then Tc (or overturning moment at Dc) = 0.5DcX 9,000 lbs. X No. of bolts X area of 1 bolt in sq. in. {Tc = DcT-i-Db). Lining: Where temperatures are above 600** F., fire-brick linings are used. Linings are generally 9 in. thick for lower 30 ft. of stack, and 4 in. thick above that height. 1 cu. ft. brick (red or fire) weighs about 120 Ibp 168 APPENDIX. ENEBGT AND THE TRANSMISSION OF POWER. Screws for Power Transmission (Screw-Presses, etc.). Square threads are preferable to V threads, and the moment to raise load W where r^mean radius of thread, j?"™ pitch, and /i = coeff. of friction be- tween nut and screw. Let n==No. of threads in nut, the projected area of which -0.7854n(di2-d22). and W = 0.7S54np{di^-d^), where d, and (h are root and outer diams. of thread, and ?=> allowable pressure in lbs. per sq. in. of projected area, =125,000-5- V, where K = rubbing speed in ft. per min. and ^100. (p = 80,000 -*-V when F = 400.) These values of p are for W. I.; for steel, multiply same by 1.2. ^=0.07 for heavy machine- oil and graphite in equal vols., =0.11 for lard-oil, =0.14 for heavy machine- oil. Efficiency: Let a = pitch angle at radius r, (tan a=p"-5-23rr), and 6= angle of friction, (tan ^ = ;t). Then, efficiency = tan a-J-tan(a-f ^). For max. eflf.. make a '=45° — 0.5^. In order that load may not overhaul, o must be less than 4>, and the efficiency cannot then exceed 50%. Piston-Bods, Connecting-Rods, Eccentric-Rods. Euler's formula for compression (both ends free) is : P^n^EI-i-P, where P = total pressure or load in lbs., Z = length of rod in in. (/■*icd*-«-64 for circular sections; / = 6*A-i-12 for rectangular sections). Substituting in formula, introducing a factor of safety «, and taking E = 29,000,000 for W. I. forgings, P = 2i^,000,000 d<-5-2«t=' tor circular sectiuna, and P = 23,800,0006»A-«-«Z^ where rf^diam. in in., 6 and A = breadth and height in ia.,—d. 6, and h being taken at mid-length. For piston-rods, « = 8 to 11 when load fluctuates between P and 0; « = 15 to 22 when load fluctuates between +P and ~P. (For very large horizontal engines the deflection of rod due to weight of rod and piston should be considered, and it should not exceed 0.15 in.) For eccentric-rods «»40, for connect- ing-rods « = 26 and 15 respectively for circular and rectangular sections. h at mid-length = 1 .756 to 26 (heights at crank and cyl. ends»1.2A and O.Sh, resp.). d tapers to 0.8d at crank end, and to 0.7d to 0.75^ at cyl. end) . For very low speeds (drc. section) «=33; for sudden chants in direction of P (as in pumps), «=40 to dO. For high speeds, as m locomotives (rect sections), A = 26 « = 6.6 to 3 3 (See also Columns, Ehiler's formulas, ante.) Connecting-Rod Ends (Marine type, rod formed with a T-end, brasses being held to T by bolts and cap). Biam. of each bolt at bottom of thread. d=0 02v^, where P = ^ max pressure on piston in lbs. Thickness of cap and T on end of rod, <=1.4d. These values of d and t are for W. I.; for steel take 90% of same. Piston-Rings. Radial depth, A = 0.033d when bored concentrically, =0.04d opposite joint when bored eccentrically (tapering to 0.7A at ends). Width = 2A; overlap of ends = 0. Id, where d=aiam. of cyl. Stufflng-Boxes. Inner diam. of box=depth=d+(0.8 to l)v^ where d — diam. of rod Pedestals (d = shaft diam., 7 = lensrth of brass, both in in.). Diam of bolts for base and cap = 0.25d4-0 125 in.; dist. bet. centers of cap-bolts = 3.3d -I- 1 .65 in. ; do., ba.se-bolts = 3 5^ -^ 1 .T.'i in . : width of ix'destal = 0.72Z. Thicknesses: cap, 0.375d; base-plate, 0.25d-f- 0.125 in.; metal around cap- bolts and brasses, 1.8d + 0.09 in. (If d<7 in., use 4 bolts each for base and cap.) Brasses: thickness at center = 0.08d -I- 0.125 in.; do., at sides, 0.06d + 0J in. JiMirnsil Bearingfi. Allowable pres.s^.. , . ) per sq. in. of projected area (iXd): Journal. Beaiing. p. Crucible steel (hardened) Crucible steel 2,100 lbs. '* " (hardened) Bronze 1,250 •• (soft) 850 APPENDIX. 169 Journal. Wrought iron, polished W. I. or C.I. W. I. (water lubrication) Bearing. Bronze C. I. or bronze Lignum VitaB 570 425 350 350 Speed. Moderate High Moderate High Main bearings, Crank- and croBs-head pins, locomotives, Crank-pin for punch and shears. Crank-pin Cross-head pin 900 550 1,100 700 200-360 1,400, 2,100 resp. 2,800 and up (Bach.) 1,800-2,100 350 300 1,000-1,500 Main rods of locomotives, Freight-car axles, i / = 1 8d I Passenger-car axles, > ( Neck bearings of sheet-mill rolls. (Eng'rs Soc. of W. Pa.. Dec. '05.) Main bearings of engines, c+V^v [tj = vel. of rubbing surface in ft. per sec; c=600 for vertical engines, =376 tor horizontal. (Edwin Reynolds.)] pF<50 000; p = 30 to 80 lbs.; F = 400 to 1,200 ft. per min.; l = 3d Allowance in diam. for oil-film = 0.001 (d+1) in. for d^5 in. Allowance — 0.001 (d+4) in. for d>5 in. (Gen. Elec. Co. Practice.) Thrust-bearings: pr = 40,000 to 50,000, with loads up to 1,000 lbs. per sq. in. of projected collar area. Worm-gears: pV = 60,000 to 75,000 for max. efficiency, the higher value for high values of V, and where helix angle = 20°; worm of hardened steel, wheel of phosphor-bronze. For electric-elevator work y = 600 to 1,000 ft. per min. Large shaft-bearings tested by the Westinghouse E. & M. Co., over runs of 7 hoiufl yielded the following unusually high values for pV: 9-in. shaft, 150,000 to 500,000; 15-in. shaft, 260,000 to 840,000 (p = 140 to 170). Lower values for each size were when heavy machine oil was used, higher values with paraffin oil. (A. S. M. E., Dec. '05.) Friction Couplinj^s (C. I.). Shaft diam. = d; hub diam. = 2d; depth of groove = id; width of groove = i^d; width of friction-cone faces = lid; thickness of wheel webs=«|d; angle between shaft and cone faces = 4** to 10^ Claw CouiHlngs (C. I.). Diam. of both claws, D = 2.1d+2 in.; diam. of fixed hub = 1.6d+1.6 in.; length of fixed claw = 0.9d + l in.; depth of recesses in both claws = 0.64 +0.6 in.; length of fixed hub = 0.5d+0.5 in.; length of sliding claw = 1.7d+1.7 in. (of diam. D throughout length); depth of groove midway between end and recess = 0.3d + 0.3 in.; width, do.,=» 0.5d + 0.5 in. (d=diam. of shaft). Roller Bearings. For heavily loaded, slow-running joiu'nals, P= 2,100nW for hardened-steel rollers (Ing. Taschenbuch). The coefficient of friction for roller bearings is from 0.2 to 0.33 of that of plain bearings. (C. H. Benjamin, Machinery, Oct. '05.) Mossberg bearings (rollers confined rigidly as possible in a cage): Safe load in lbs. = cnW, where c=250 for rollers up to | in. diam. (c = 300 to 350 for larger rollers) . / (generally) = 1 .5 X shaft diam. D. For I) up to 1 2 in., diam of roller d = 0.104D; above 12 in., d = l| to li in. n (approx.) = 27-(1.6-4-d) for d<li in.; n = 90-(80-^d) when d>li in. Take nearest even number. Ball Bearings. Max. allowable load on one ball in lbs., P='C€p. Values of e: For C. I balls between two planes, c = 35; steel balls on plane, coni- cal, or cylindrical surfaces, c = 700 to l.OdO; steel balls in rac^s whose radius of curvature = fd, c=l,4O0 to 2,100. Above values for continuous use; for intermittent use c = twice lower values given (d = diam. of ball in in.). Total allowable load on bearing = 0.2P X No. of balls (Bach and Stribeck.) According to C. O^gauff (L' Industrie Elrdrique, 7-25-'05) the least power is lost in friction when d=(D^-7)+0.08 in., where D= inner diam. of race in in. Max. allowable load in lbs. for an annular bearing, P= 84,000D-s-(JVD + 375), where i\r = r.p.m. 170 APPENDIX, For a 2-point bearing, the coeflf. of friction, /i» 0.0015; for 3-point, 0.003 to 0.006; for 4-point, 0.015 to 0.06 (which is no better than a plain bearing). The friction loss is constant up to linear speeds of 2,000 ft. per min. Above 17,000 r.^.m. centrifugal force causes the balls to slide on the shaft instead of rolling. Bevel Gearins. (7 » angle between shafts «> a +/9, where a and p are angles made by the shafts and elements in their respective pitch cones (a for larger gear). Let ^=-180° — tf, and r=aii8lelto be added to a and B to give face angles of gears Then, if (? < 90**, tan ;? = r -i- fr cot tf + (fl -s- sin <?)] ; if tf = 90^ tan^ = n-*-]V; if tf>90^ tan /9=r+[(fl-f-8in ^)~r cot ^]. a- — ^'. tan r = 8in;9 + 0.6n. Face angles = a + r and P + r for larger and smaller gears respectively i)— i)i+i)2 cos a; d!=di+i>2 cos)?. (D, d — outside diams.; Di, di» pitch diams.: iJj™ working depth of tooth; ft, r=- pitch radii (=0.5i)if 0.5ai); N, n»No. of teeth. Capital letters for larger gear.) The cutter for larger gear should be the proper one to cut N\ teeth, whert; JVi = JV-i-cos a; for smaller gear, the one to cut tii teeth, where ni=» n-*-cos /9. Spiral Gears. Let angle that teeth make with a line parallel to axis of gear=»tf. Then, normal pitch T = p"costf (where ©" — circumferential pitch), and p"=T-f-cos <?. Let Pd =■ diametral pitch, JV=»No. of teeth in a spur-gear of pitch radius r, and N\ = No. of teeth in a spiral gear of pitch radius r. Then, N - 2rPd, and Nx = 2rPd cos 6. Pitch diam. - .Yi + Pd cos tf ; outside diam. = pitch diam. + (2 + Pa)- The teeth of spiral gear should be cut with a spur-gear cutter which is correct for N2 teeth, where JV2=(No. of teeth in spiral gear) -«- cos* tf . r and n (page 50) = (90°-«) and (90* -«i) respectively, Worm-Gears. Involute gears of more than 27 teeth, and having ad- denda of 0.25p", yield favorable results for pitches not exceeding 18°. Allowable pressure on teeth, P(in lbs.)«c&2>", where 6 — width of tooth in in., and p" = pitch in in. c=-250 to 400 for cast-iron (=-450 to 700 for phosphor-bronze wheel and hardened-steel screw). Worms whose threads make an angle > 12.5** with a normal to axis of worm generally run well and are durable. (Halsey.) Diam. of worm wheel at throat — 0.3183 X (No. of teeth + 2) X pitch of worm in in. Power Transmitted by Worm-Gearins. p* = {aF^ + &F + c) -»- JV, f 01 single thread, where p = pitch of teeth in worm wheel in in., F — H.P. trans- mitted, and iV = r.p.m. For F>3 HP., 0-4.74, 6-113, C--106; fo» F<3 HP., a-22. 6 = 25, c = 2. For double, treble, and quadruple threads take 2N, ZN, Ali, respectiv^ for denominator of formula. Greatest pitch diam. of worm, d^Y7.2p-i-F^ for single thread. For double, treble, or quad, threads miiltiply formula value of d for single thread by 2, 3, or 4. The foregoing is for finished worms and gears; if rough, cast teeth are used, multiply values of p and d obtained from formulas by 1.33 and 0.8, respectively. (Derived from practice of Otto Gruson & Co., as stated by W. H. Raeburn, Am, Mitch., 4-19-'06) Flat-Link Driving Chain (Steel). Load in lbs.— P: end diam. of pin, d= (2.4P + 6,100) -!-(P + 27,000); diam. of pin bet. links -1.25d for small sizes (ranging to 1.1 2d for large sizes); width of link — 2.5d; len^h of pin bet. links -1.65d+ 0.22 in. (for d<l in.), or 2.62d-0.7 in. (for d> 1 in); length, c. to c. of pins — 2.7d + 0.16 in.; over-all length of link>» 4.4d + 0.l6 in. No. of plates, i(^i on each side): When P- up to 1,000 lbs. 1,000 to 4,500 4,500 to 13,000 larger i- 2 4 6 8 Thickness of each plate = (3.1 7P + 3,900) + t(P + 29,000) . (Derived from data on a chain extensively used in Cxermany.) Pulleys (C. I ). Width of face. 6, = (l.lXbelt width) -I-0.4 in.; thick- ness of rim at edge— (0.01 Xradius of pulley) +0.12 in. Crowning: diam. of pulley at center is Q.\2'^hi greater than diam. at edges. No. of arms — 0.7^5. For oval arms h (long axis of ellipse)— v^l.256<d-*- No. of arms. hx (short axis)— 0.4A. h and ^ii (at hub) taper to 0.8^ and O.8A1 at rim (6 = belt width, < — belt thickness, d — diam. of pulley, — all in in.). Lenirth of hub — &i, when 61 > 1.2 to 1.5 X shaft diam. (for narrow faces); for wide APPENDIX. 171 faces, length may be less than &i. For loose pulleys make length of hub-* 2 X shaft diam. If &i > 12. in., use two sets of arms. Pulley Blocks and Sheaves. Diaineters are taken considerably less in hoisting work than for power transmission. The Ing. Taschenbuch gives Uie following: Dia^. of sheave =cX diam. of rope, where c=20 for wire rope and 8 for hemp. Brakes (Fig. 40). Let W = pressure on brake lever in lbs., P = brak- ing force at rim of wheel in lbs., /£ = coeff. of friction <0.6 for wood or leather on iron (dry surfaces) » 0.18 to 0.25 for iron on iron, diminishing with increase in vel. For block brakes (I.) Tr= . . „ (— ±-5) ,theminus A + i> ^ H D' sign being used for rotation indicated, — ^plus for opposite. For B+C^n, }^Z^S-^ A\ V ") .^^ j w Fio. 40. W — 0, or the brake is self-acting; B-*-C is therefore made > ft. For dotted position, C is neg^ative and signs in parenthesis should read =F . For opp. direction of rotation, B-s-C should be <At. Band ^rakes: Let c^base of hyperbolic system of logarithms "2.71828; a — angle spanned by the arc of contact of band with wheel; t and 6 — thickness and width of band, and /< = allowable unit stress in band. Then Tin II .) tension T = P^ (cA'a - 1 ) ; and t = PeMa + (e^a - 1), for direction 1 (for direction 2, interchange values of T and t). Band cross-section » bt =» Pefi«-i-ft(e/^oc-\), where /< = 8,500 to 11,000 lbs. per sq. in. (t is generally about 15 in., — b not more than 3 in.). If ft is taken «= 0.18 and a-f-2>r=0.7 (generally), then r = 0.83P and t = 1.83P, for direction 1. Fora + 2»=0.1 0.3 0.5 0.7 0.9 em =-1.12 1.40 1.76 2.21 2.77 In 11; W''TC-t-A',in III, W^tC + A. W ia least when end with lesser tension is attached to lever, as T in II (direction 1) and / in III (dir. 2). Differential Brake (IV): W^(TC-tc) + A=P(C-ce/'<')-i-A(ef^-l). If C'=ceP«, W = 0; C is generally taken>ceA*«. (For a + 2«-0.7, •C-2.5c to 3c.) For alternating directions of rotation (V), W ^ PCief^ot + 1) ■*■ A(e/*«—l), A block brake is preferable to this arrangement. 172 APPENDIX. HEAT AND THE STEAM-ENGINE* Properties of Saturated Steam (below Atmos Pressure). p, abs. ^^F. V. w. H. h. L. .089 32. 3.387 .0002952 1091.7 0. 1091.7 .126 40. 2,717 .0003681 1094.2 8. 1086.2 .25 59.5 1,270 .0007874 1100. 27.5 1072.5 .50 80. 640.8 .00158 1106.3 47.8 1058.5 .75 92.5 442.6 .00226 1110. 60.6 1049.5 1. 101.99 334.6 .00299 1113.1 70. 1043.1 2. 126.27 173.6 .00576 1120.6 94.4 1026.1 4. 153.09 90.31 .01107 1128.6 121.4 1007.2 6. 170.14 61.67 .01622 1133.8 138.6 995.2 8. 182.92 47.07 .02125 1137.7 151.5 986.2 10. 193.26 38.16 .02621 1140.9 161.9 979. 12. 201.98 32.14 .03111 4143.6 170.7 972.9 14. 209.67 27.79 .03600 1145.8 178.3 967.6 14.7 212. 26.42 .03794 1146.6 180.9 965.7 Superheated Steam. According to Linde (Z. V. D. I., Oct. 28, '05) the PV law may be expressed as: 144p(t> +0.261)= 85 .86t, where p=lb8. pressure per sq. in., r = cu. ft. in 1 lb. at the pressure p, and t=* absolute temperature in degs. F A formula which expresses the results of his experiments to determine kp is: kp'=0A62 + p(^-^-r^—0.OO022\ p and t as above. Herr Bemer (Z. V. D. I., 9-2-*05) states that Linde's values for kp are confirmed by his own observations, those of Lorena being from 20 to 25% too high. He further states that the cost of lubrication is slightly higher than when saturated steam is used, that the resistance to flow in a superhefiter coil » 1 .2 X resistance of smooth pipe, and that the resisjAnce of a valve fully open is equal to the resistance of about 56 ft. of smooth pipe. The velocity of flow m en^ne passages may be as high as 12,000 ft. per min. (Amdtsen, Z. V. D. I., ll-25-'05.) Corliss Valves, Dash-Pots. Diam. of valve=cXoyl. diam., where c=0.25 for valve on high-pressure cyl. ( =0.2 for low-pres. cyl.). Dash-pot diameters are about 0.8 of the diams. of their respective valves. Steam Consumption of Compound Eng^ines, high-grade, at full load -15.6 lbs. per kilowatt-hour (=«11.5 lbs. per H.P.-hr.) at 170 lbs. gauge pressure, 90* F. superheat, and 26 in. vacuum. (Averages by Stevens & Hobart, Power, Dec. '05.) Prime Movers for Power Plants. In a high-grade power plant about 10.3% of the heat unitfl in a pound of coal are delivered to the Dus-bars in the form of electricity It is possible to raise this thermal efficiency to about 14.4% (with steam-turbines to 15%) by reducing the losses due to the stack, boiler radiation, and leakage, and by using superheated steam. Where the load-factor exceeds 0.25, economizers should oe used. Auxil- iaries should be steam-driven, with exhaust into heater. The friction loss of a 7,600 HP engine recently tested was 6.35% of the H.P. generated. Large gas-engines can convert about 24% of the energy of coal into electric energy, the chief objection to their use being with regard to overloads. This objection may be overcome by a suggested combination of ^as-engines and steam-turbines (utilizing the waste heat of the gas-engines m the pro- duction of steam), which would yield an average thermal efficiency of 24.5%. Comparative cost of maintenance and operation of plants per kw.-hr.r Gas-engines and tur- bines. 46.3 91 Steam- Steam- Gas- engines turbines. engines. Maintenance and Operation 100 80 51 Relative Investment 100 83 100 K. Ky. 17-19 19-16.6 K 6-21. 5 15-12.6 21-23 12.6- 9 21-23.6 11.6- 7 26 7- 6 APPENDIX. 173 Marine Steam-Engines. The Screw Propeller. The pitch of a screw is the distance which any point in a blade will advance in the direction of the shaft or axis durins one revolution, the point being assumed to move around the axis and without "shp " Propellers are generally provided with four blades (naval vessels and small high-speed boats with three). The blades are generally inclined backward from the vertical from 8° to 20** (accordinig to the r.p.m.) in order to throw the water to the rear and to increase the efficiency. The indicated thrust of screw, r=(I.H.P.X 33,000) -f--YP, where ^- r.p.m., and P = pitch in feet. The mechanical efficiency of the shaft trans- mission varies from 0.8 for engines of about 600 H.P. up to 0.96 for large ones. The mechanical efficiency of the screw— Useful work of axial thrust -s- Shaft perfor mance = 0.6 t o 0.7 for best conditions. Diam. of Screw in ft., D^K ^^I.H.F. + iOmPNy'', Total area of blades (developed) = K,>/l.H.P.-*-JV; P varies from 0.9D to 1.6D. Speed V is measured in knots (1 knot = 6,080 ft. per hr.). V. Cargo Boats, 8-13 Passenger and Mail Boats, 13-17 Do., very fine lines, 17-22 Naval Vessels, 16-22 Torpedo Boats, 20-26 The Apparent Slip (in per cent) S=(C-V)-t-100C, where C-PX60JV+ 6,080. 5 =—2 to +8 for slow freighters, —8 to 16 for passenger and mail steamers, =13 to 20 for naval vessels, =20 to 27 for small, fine-lined boats. Strength of Blades: — The indicated thrust T (divided by the number of blades z) acts at a distance 0.36i> from the center of shaft and causes a T bending moment Bnt- Bm="«-(0.36i) — distance from c. of shaft to root of blade). For a parabolic segmental cross-section (length I, thickness h) oblique to axis, the Moment of Resistance » 0.076//l^ and consequently / = Bm+0.076i/i2 / (safe) in lbs. per sq. in. = 7,800 for cast steel, =6,700 for bronae, =2,800 for C. I. Thickness of blades at tips =0.25 to 0.8 in. for bronse, and 0.6 to 1.2 in. for C. I., according to size ol the screw. Indicated Horse-Power of Engines. I.H P. = pmLa(2JV)-+- 33,000, where a = area of low pressure cyl. in sq. in. pnij the mean effective pres- sure, depends on the absolute boiler pressure p, and also on the number of expansions: , A .- 1\ , vol.of steam admitted into h. p. cyl. Pm^fcpcv 1+ log. — j. where c — ; 5 i r i 1 . >^ *^\ *« c'' 1. p. cyl. vol +h. p. cyl. vol. k has the following values at ordinary speeds: Compound-Engines, 0.66 to 0.7 (at higher speeds, 0.6 to 0.66) Triple-Expansion, 0.55**0.6 (" ** " 0.62 " 0.68). Quadruple-Expansion, 0.52 ** 0.64 Total Number of Expansions ( = l-i-c): Compound, small boats, 6 to 6; do., freighters, 7 to 8. Triple-Expansion, torpedo boats, 6 to 7; do , naval vessels, 6.6 to 8; do , express and freight steamers, 8 to 10. Quadruple- Expansion, express steamers, 10; do., freight steamers, 11 to 13. Cut-ofF in high-press, cyl is at about 0.7 stroke (0.6 stroke for slow boats). Piston Speed and Bevs. per Min. Speed, ft. permin. R.P.M. Torpedo Boats, 1,000-1,200 300-400 Armored Vessels, 800-1.000 100-150 Express Steamers, 800- 950 76- 95 Large Passenger Steamers, 700- 900 70- 90 •• Freight 700- 800 70- 85 Small •• 600- 750 96-130 •• passenger " 400- 600 160-200 174 APPENDIX. Steam Velocities (ft. per min.). Main steam-pipes, 6,000-8,000; steam passages: h. p. cyl., 5,000-6,000; intermediate cyl., 6,000-7,000; 1. p. cyl., 7,200-8,600. For exhaust take 80% of above values. For small engines these velocities may be increased 20%. Cylinders. Thickness of walls (cast iron) t= - ^90-4-10 "^^-^ *^' where p— gauge pressure in lbs. per sq. in at h. p. cyl., and d—diam. of h. p. cyl. in in, (This value of t is for h. p, cyl. with or without jacket and also for intermediate and 1. p. cyl. linings. Cylinders without hnings should be 0.2 in. thicker to allow for reboring.) Thickness of cylinder head ti=t (for cast iron, head ribbed) =0.6< to O.Q&t for cast steel. Diam. of cyl.-head studs = <; pitch of studs — 3<, 5.&t and 6.5t for high, intermediate and low-pressure cylinders, respectively. Thickness of cyl.-head flange =»=1.2t, width = 2.6t to 3.3t. Relief valves (for both heads) should have a diam. = (i^, 1*7, ^)Xdiam. of (high, intermediate, low-pressure cyl.). Valves shoma open at about 8 lbs. above p. Pistons. (Cast steel, coned, concave toward crank). Thickness near center, < = 0.0043d'^^^+c; thickness near rim = 0.5< to 0.7t. c— 0.24 in., 0.36 m., 0.48 in., respectively, for h., i. and 1, pros. cyls. p=boiler pressure in lbs per sq. m. for h. p. cyl., = 46 X boiler pressure for intermemate cvl., = 0.2 X boiler pressure fori. p. cyl. For forged steel take i of above formula value for t. Piston-Rods. (Medium hard steel, end tapered and fastened to head by nut.) Area at root of thread in sq. in. ^ (p Xarea of h. p. cyl. in sq. in.) •♦•7,000. (For naval vessels and torpedo boats substitute 10,6(X) and 12,600 respectively for 7,0(X)). Full section of rod beyond taper =» 2 X area at root 01 thread. Connectinn^-Bods. Length = (2 to 2.25) X stroke. Diam. at piston end = diam. of piston-rod, approx.; diam. at crank-end = (1 .1 to 1.4) X diam. of piston-rod, according to length. . Bearings. The crank bearing is lined with white metal of a thickness » (0.025 X diam. of bearing) +0.2 in. Thickness of cast-steel bearing cap at the middle = (0.17 to 0.24) X diam. of bearing. Shaft bearing: thick- ness (cast iron) =0.1 2d +0.2 in.; for bronze, thickness = 0.09rf + 0.1 2 in. Thickness of white-metal lining = (o.2 + — ) in. d= shaft diam. in in. 16 7* 1 Crank-Shafts (forged steel): d"=— . -^ . ^— -, where d =» outer diam. of shaft in in. (di= inner diam. in case of a hollow shaft), Tm" turning moment in inch-lbs. = 63, 025 X I. H. P. -4- iV. /«afc (average) in lbs. per sq. in.==6,6(X) for torpedo boats, *» 6,700 for naval vessels, —4,600 for mail steamers, =4,(X)0 for freighters (max. and min. values are equal to average values ±10%). Crank-Throws. Outline described in part by circles (of diam. = 2d) from centers of shaft and crank-pin, connected with filleting curves of radii = d. (d-diam. of shaft). Thickness of throws = 0.6d to 0.7d. The shaft is enlarged ^ of its diam. in the throw. Thickness of flanges on shaft =0.26d to 0.28d. Length of bearing -5- diam. of shaft = 1.4 to 1.6 for torpedo boats, =1.1 to 1.4 for naval vessels, =0.9 to 1.2 for other vessels. Surface Condensers. Cooling surface in sq. ft. required per T.H.P.: Compound, 5 to 6; triple-expansion, 3.6 to 6; quadruple-expansion, 3.5 to 4.6; torpedo boats, 26 to 32. (The lower values given are for naval ves- sels.) CJondenser tubes are of brass, tinned inside and out, f to i in. out- side diam. and about 0.04 in. think. Air-Pumps for Surface Condensers (Single-acting). Volume = cX vol. of 1. p. cyl. c = tV to tV for compound; =^ts to ^ for triple-expan- sion; = ^x to 3*1 for quadruple-expansion. For injector condensers. Vol = (i to ♦)Xvol. of 1. p. cyl. Surface Condensers of Hlich Efficiency. By passing the condensing water several times through the tubes (arranged in groups), and by pro- \ading for the thorough drainajre of the water of condensation so that *he tubea are not continually subjected to showers of water particles which APPENDIX. 175 impair the surface contact, Prof. R. L. Weighton has designed condensers to be' used in connection with dry air-pumps which condense 20 lbs. of steam per hour per sq. ft. of surface, condensing water required being 24 times the amount of feed-water used. He has effected a higher sur- face efficiency — 36 lbs. per hour per sq. ft., — but the condensing water required in this case is equal to 28 times the feed-water. Vacuum in both cases is 28.5 in. of mercury, feed-water temp, at inlet = 50® F. For a system with tight piping, capacity of air-pump » 0.7 cu. ft. per lb. of steam condensed per hour. The condenser tubes are provided with tri- angular wooden cores in order that the water may meet the tube sur- face in thin streams. Temp, of hot-well may be 3° to 5° higher than that corresponding to vacuum (up to 29 in.). Ctroalating Pumps Kl^ouble-acting). Vol. = 0.025 X vol. of 1. p. cyl. (approx.). Boiler Accessory Apparatus, Feed' Water Heaters. Let t and T » initial and final temperatures of water in degs. F. [average temp. — (t + T) ■*- 2]. B.T.U. transmitted per sq. ft. of surface per hour, per degree difference of temp. = c-= 180 for water-tubes, 200 for coils, and 114.5 for steam-tubes (usually 2 in. diam.). Let Ta-temp. of exhaust ( = 212° F. generally); then, B.T.U. per hour per sq. ft. =c(3r»— 0.5;,< + r)]; lbs. steam condensed per sq. ft. per hour = ciT8—0.5[t + T)]-i-9e6. Velocity of water in tubes in ft. per min.: single- flow, 8.33; double-flow, 12.5; coils, 140. Sectional area within shell =" cX total cross-section of tubes, where c = 6.3 to 9 for water-tubes, =7.5 to 10 for steam-tubes, — the higher values for variable loads. For coil heaters, sectional area within shell = (11 to 8) X cross-section of exhaust pipe, inversely according to the capacity of heater. Open heaters with trays or pans: Volume of shell in cu. ft. = Capacity in H.P.-^c, where c = 2.2, 6, and 8 for very muddy, slightly muddy, and clear water respectively. Tray surface in sq. ft. = lbs. water heated per hr.-^c, where c = 118, 166, and 500 for very muddy, slightly muddy, and clear water respectively. These values for tray surface are for vertical heaters; for horizontal type of heater the values of c are about 8% lower. Sipbon or Barometric Condens ers operating on the principle of injec- tors: Diam. of exhaust pipe 'min.,d = V c X lbs. steam to be condensed per min., where c=0.81 when wt. of steam is less than 20,000 lbs. per hour ( = 0.6 3 if greater than 20,000 lbs. per hr.). Diam. at throat in in. = ^Ww-*- 17,210; width of annular opening through which water is admitted = Wip + 39, 550d (Tr = lbs. steam to be condensed per hr., to = lbs. water required to con- dense 1 lb. of steam). Air- Pumps for Stationary i:ng:ine8. Single-acting: vol. in cu. ft. = 0.0328+ N; double-acting: vol. in cu. ft.=0.016/S-5-iNr. iS = lb8. of steam condensed per hour, and JV = r.p.m. (Ing. Taschenbuch.) liocomotives. Elevation of Outer Rail on Curves. E (in ft.)^0.06688(?F2-!-i2, where G^» gauge of track in ft., V = velocity of fastest train in miles per hr., and i2- radius of curve in ft. («. R. Gazette, 3-16-'06.) Combustion. N*taral-G*s Fuel for S team-Boilers. The same economy is ex- hibited with a blue flame as with a white or straw-colored flame, but the latter affords greater capacity. One boiler H.P. may be expected from 43 to 45 cu. ft. of gas (at 60° F. under a pressure of 4 oz. above 29.92 in. of mercury). Fuel costs are the same with natural gas at 10 cents per 1,(X)0 cu. ft. and semi-bituminous coal at $2.87 per ton of 2,240 lbs. (J. M. Whitham, A. S. M. E., Dec. '05.) Efficiency «f Combustion. The higher the percentage of CO2 in the gases es'-apini? into the chimne^', the higher will be the efficiency of the furnace, and the production of CO2 may be forced until the presence of CO indicate incomplete combustion. In good furnaces 10 to 15% of CO2 176 APPENDIX. may be realized. The approximate fuel loss (in per cent) due to incom- plete combustion = 0.4(<2-^i)^- (per cent by volume of CO2), where <2"= temp, of chimney gases and tt = tecop. of air entering the furnace (both in degs. F.). An instrument called a CO2 recorder indicates and records con- tinuously the percentage of that gas present Mechanical stokers do not accomplish any marked saving of fuel over careful hand firing in plants where less than 200 tons of coiJ are used per month, but they yield much better results than average hand firing, are easily forced, maintain a uniform steam pressure, and assist greatly in the smokeless combustion of soft coals. They are adaptable to all kinds of solid fuels, and in this respect promote economy, for it often happens that a cheap, low-grade fuel may be employed, whereas with hand-firing . a more expensive quality would have to be used. Incrustation and Corrosion. Boiler Purges. Caustic soda and lime-water combine with the car- bonic acid contained in water (in combination as bicarbonates) and pre- cipitate calcium and magnesium carbonates. Soda ash acts on the bicar- bonates of lime and magnesia, [forming bicarbonate of soda, which is decomposed by heat into CO2 and sodium carbonate, the latter being precipitated. Sodium aluminate and sodium fluoride are also used in waters contain- ing bicarbonate of lime. Trisodium phosphate is used where water contains sulphate of lime, precipitating sodium sulphate and calcium phosphate. Internal-Combustion Engines. Gas Producers -are closed furnaces in which the fuel is burnt with a limited supply of air and steam, resulting in the production of gas. The air and steam are either forced (pressure producer) or drawn (suction pro- ducer) through a bed of incandescent coal or coke. The O of the air first combines with the C of coal to form CC)?- This passes up tnrough the incandescent coal and changes to CO. When steam is mixed with the air and meets the burning fuel, H is liberated and the O of steam com- bines to form more CO. These, with the N of air and the volatile part of the fuel (CH4) make up the resulting fuel-gas. Theoretically the best temperature is about 1,900** F. 1 lb. of coal with upwards of 0.7 lb. steam will yield from 65 to 75 cu. ft. of gas (135 to 140 B.T.U. per cu. ft). Pres- sure producers are used for engines 01 over 200 H.P. In these the air and steam are furnished under a pressure of from 2 to 8 in. of water. The hot gas passes through an economieer where it preheats the air used and also gives up heat for the generation of the steam required. It then pai»es through the scrubber (vessel provided with irays of coke upon which water streams from above) and thence to the purifier (another vessel pro- vided with trays of sawdust, and also with oxidised iron-filings when sul- phur is to be removed from the gas). The best results are obtained from anthracite (pea size or larger) having less than 10 to 15% of ash and but little moisture. If the fuel contains more than 5 to 8% 01 volatile matter, it will cohere and prevent proper working of producer. Coal with an ex- cessive amount of ash tends to choke up the air-passages. Grate surface per H. P. =6 to 8 sq. in. (the latter for producers of less than 25 H.P. capacity). The volume of producer per H.P. = 0.11 cu. ft., approx. (firing intervals of 3 to 4 hours), for anthracite, and 0.18 cu. ft. for coke. Vol. of scrubber = 0.9 to 1.1 cu. ft. per H.P. Vol. of purifier = 0.36 cu. ft. per HP. In ordinary generators about 85% of the heat of the fuel leaves the producer, a loss of 15 to 20% being due to heating, radiation, and unbumt resi(hie. Efficiency, 65 to 75%. Suction-Producer Tests of a number of plants in London using Scotch anthracite (pea) showed a consumption of 0.85 to 1.1 lbs. per B.H.P. hr. for full load, and 0.9 to 1 .25 lbs. at half load Garger values for 8 H.P., smaller for 20 H.P.). Volume of producers in cu. ft. per H.P. =0.23 (for 20 HP.) and 0.26 (8 HP). R.P.M., 200; mechanical efficiency, 81 to 84% at fuU load (69 to 71% at half load). M.e.p. about 79 lbs. APPENDIX. 177 Blast-Fumace and Coke-Oven Gases. For each ton of iron smelted about 88,000 cu. ft. of blast-furnace gas are liberated. One ton of coal in coking yields about 8,800 cu. ft. of coke-oven gas. /Hot Tubes require from 6 to 7 cu. ft. of illuminating gas per hour (or 0.22 to 0.33 lb. gasoline per hour). Denatured Alcohol is ethyl alcohol rendered imfit for consumption as a beverage by the addition of wood-alcohol, benzol, etc. It burns smokelessly with a hot, non-luminous flame, and the products of its com- bustion do not yield an unpleasant odor unless the percentage of benaol is excessive. Ethyl alcohol (C2H6O) is made by the fermentation of sugars or starches contained in molasses, com, potatoes, etc., with which malt and yeast are combined. Starch + Water = Dextrose = Alcohol +Carb. dioxide. (C6Hio05)8+H20 -CeHiaOo =2(C2H60) + 2(C02) The alcohol is distilled off by the proper application of heat, absolute alcohol (100%) being that in which no water is present. Specific Gravity of Ethyl Alcohol at 59°|F. Approx. Lower Heating Value. % by vol. % by wt. Sp. g. 100 100 .7946 11.700 B.T.U. per lb. 95 93.8 .805 10,900 90 87.7 .815 10,100 One gal. abs. alcohol = 6 . 625 lbs. 77,500 " '* gal. Composition of absolute alcohol = 0.522C4-0.13H + 0.348O. Air required for combustion of 1 lb. alcohol = 9 lbs., or 111.5 cu. ft. at 62** F. Boiling-point = 173.1** F. freezing-point = -200° F. Specific heat of liquid at 32'* F. =0.5475. kp of vapoT = 0.4534; kv = OA\ fcp-*-A;r=n = 1.14. Law of compression: Pyi.M=PiF, 1.14 Alcohol motors are started up with gasoline , and , when warmed up suffi- ciently, alcohol vapor is used. Cooling water required is about 20 lbs. per H.F. hour, and efficiency is promoted by having its temperature as nigh as possible. Denatiu'ants. Sp. g. Boiling- Lower Heating Value (59° F.) point. (Approx.). Methyl (or Wood-alcohol). . .CH4O 0.800 151° F. 8,300 B T U. per lb. Benzol CeHe 0.866 176° 17,200 Acetone CgHeO 0.800 133° 12,600 '* " •• Pyridine CgHsN 117° 17,000 GasoUne 0.700 180-210° 19,000 " " *' Denatured Alcohol Mixtures [parts by volume added to 1(X) vols, of 90% (vol.) alcohol]. Sp. g. CH4O CsHsN CgHeO CeHe Gasoline French 0.832 7.5 2.5 0.5 German 0.819 1.5 0.5 0.5 Do., "Motor Spirit "...0.825 0.75 0.25 0.25 2 No more heat should be used than is necessary to vaporize the mix- ture, high temperatures limiting the allowable compression and decreasing the economy. For a 90% (vol.) alcohol 7.9 lbs. of air are theoretically required for the combustion of 1 lb. Assuming 11.8 lb. (an excess of 50%) in practice, 1 cu. ft. dry air (at 60° F ) is supplied for 0.(X)65 lb. nlcobol, or as 90% (vol.) = 87.7% (wt.), 1 lb. air will carry 0.877 (1-5-118) = 0075 lb. of abs. alcohol, and (1 -0.877) (1 -^1 1.8) =0.01 lb. of water If the air be considered as saturated with moisture when entering the vaporizer at 60° (26 in. mercury), it will contain 0.013 lb. water in addi- tion to the 0.01 lb. in the alcohol, or 0.023 lb. in all. A temp, of 77*^ F. Kerosene. Alcohol (90% vol.). 18,600 13 1.88 0.8 0.725 10,100 15 2.21 0.816 0.803 18. 14,140 1.446 31.7 8,030 1.758 178 APPENDIX. will vaporise this amount of water and also 0.162 lb. of alcohol, con- sequently the smaller amount of alcohol actually used will be super- heated. Under these conditions (total heat of vaporization at 77° F. being 468 B.T.U. per lb.) the heat required for vaporising is about 6% of the heating value of the alcohol and may be obtained from the exhauBt, or by preheating the air used to about 270° F. The best results are obtained by compressing the mixture to 180- 200 lbs. per sq. in., the corresponding max explosion pressure being about 4S0 lbs. per sq. in. d0% (vol.) alcohol costs about 16 cents per gal. (2.21 cents per lb.) when made Irom good com at 42.4 4»nts per bushel. To compete with gasoline at 16 cents per gal. its cost must be reduced to 12 cents per gal., which *s possible through the use of low-grade grain, cheap vegetable matter, and refuse containing sugar or starch. Gasoline. B.T.U. per lb 19,000 Cost per gal. in cents 15 •• •• lb. " " 2.67 Specific gravity 0.710 • Lbs. per B.H.P. hour 0.68 • Thermal brake efficiency in per cent 23. B.T.U. per B.H.P. hour 11,000 Fuel cost per B.H.P. hour (cents) 1.485 Gas-Engrlne Desig^n. Pistons. Max. pressure on piston, P'=0.7S54pd^. Permissible surface pressure, ib — 18 to 22 lbs. per sq. in. (frequently as low as 8 lbs. where length of piston is unimportant). Length of piston l^0.llP-*-dk. (gen- erally, i«2.25d to 2.5d for smal l engines (» 1.25d to"i 6d for large en- gines). Wrist-pin diam. di=V'^/i + 5,680, where Zi — total length of piw^O.ySd; bearing length of pin is about 0.5d. Thickness of piston wall=0.02d + dei?th of packing-ring groove + 0.2 in. To provide for expansion the piston is tapered from a at the crank-end to from 0.996<2 to 0.998d at head end. Pistons over 8 in. in diam. have from 4 to 6 radial stiffening ribs. Piston-Bings. Radial depth, «=.0.022<f; width, 6-0.028d to 0.044<2. No. of rings = d-<- 66. Space between grooves = 6; depth of groove = • + (0.02 to 0.08 in.). Cylinders. Thickness of walls for strength, t=iOA2pd-*-(f — p)], where / for C.I. may be as high as 3,500 lbs. per sq. in. If d>24 in., the wall may be p-adually tapered from t at compression end to 0.6^ To allow for reboring, etc., 0.16 in. to 0.4 in. should be added to t throughout the length. Jacket: where axial forces do not enter into consideration, ti of jacket>0.4 in. If the jacket is cast in one piece with the cylinder, fi« 0.022(d + 20 for a test pressure of 420 lbs. per sq. in. (corresponding to / = 8,600 lbs. per sq. in. in a cold test). Valves. ^i=Uft in in.; di=diam. in in.; ai-^ffdi^i— area of valve opening in sq. in.; a » piston area in sq. in.; jS« stroke of piston in ft.; c=mean velocity of piston in ft. per sec; t? = mean velocity of gas through valve in ft. per sec; d — diam. of cyl. in in. Then, ai=»ac-f-t>, and, if hi < 0.25di , Kdihi - ncPNS, or dihi = d^NS + 1 ,200. v (mean) = $2 ft. per sec. If I of connecting-rod => 2.55, v(max.) = 1.6v = 131 ft. per sec. In order not to exceed this velocity each position of the piston requires a corre- sponding lift of the valve, hi > d^NS*l>-i-9,S40di, where ^ = sin a(l ±>l cos o), a being the angle made by the crank and the direction of center-line of piston-rod. * Best results obtained. APPENDIX. "^*^ 179 If ;i=0.55+Z=0.2, stroke, outward, 2 5 10 203040 45 50 return, 98 95 90 80 70 60 55 50 .304 .472 .648 .853 .962 1.011 1.018 1.014 % stroke, outward, 55 60 70 80 90 95 98 100 "" return, 45 40 30 20 10 5 2 100 .976 .892 .759 .554 .394 .251 .0 f. Thickness of valve in in. = Vprf2 j. 25,600, where d» outside diam of valve. Diam. of valveH9eat = 0.98d— 0.32 in. Diam. of valvenstem— 0.125<2 + (0.2 in. to 0.32 in.). Spring tension on valves: for throttling regulation, not less than 7 lbs. per sq. in. of cone surface; for automatic valves, from 0.7 to 1.00 lb. per sq. in. of cone surface, according to speed. Fly- Wheels. Weight of rim in lbs. - 2,165,320A;A (0.75 +p) 1.11.?.+ v^N, where p = m.e.p. on compression stroke -»-m.e. p. on power stroke =■0.3 usually; k has the values given on page 74; v=mean vel. of rim in ft. per sec, .Y — r.p.m. and K has the following values: 4-cycle. 2-cycle. One cylinder, sin£^e-acting, 1.000 0.400 ** double-acting, .615 .110 Two cylinders, twin, single-acting, .400 .4(X) " " single-acting, cranks 180° apart, .645 .085 " " double-acting, tandem or 4 twin opposing cyls., .085 — Total weight of wheel is about 1.4 times wt. of rim. (The foregoing matter has been derived chiefly from Giildner's " Verbrennungsmotoren.") Proportion of Parts* It is now customary to assume an explosion pressure of 450 lbs. per sq. in. (m.e.p. =70 lbs.) and a mean piston speed of 800-850 ft. per min. For this pressure the values given on pages 99 and 100 should be altered to the following: t of cyl. wall =^ 0.092 d + 0.25 in.; outside diam of cyl -head studs — 0.29d^/l-i-No. of studs; I of piston = 2.25d; t of rear piston wall = 0.12d; wrist-pin: length = 0.47d; diam.=0.27d; connecting-rod diam. at mid- length =0.29d; crank-pin: diam. = 0.47d, length = 0.52d; crank-throws: thickness ^O.Skf, width = 0.63c{; crank-shaft (at main bearings): diam.— 0.43rf,length = 1.12rf. Expansion must be allowed for between the jacket and cylinder walls. (For 144* F. increase in temp., a cyl. 60 in. long will expand 0.053 in. in length.) Large Gas-Englnes (over 200 to 300 H.P.) should be double-acting, tandem, in order to obtain maximum power with minimum weight. (Junge, Power, Dec. '05.) Marine Gas-Eng^ine (Otto-Deutz). 4-cyl. horizontal (20-25 H.P per cyl.); 275-325 r.p.m.; cylinder: diam. = 10.8 in., length = 33.72 m.; stroke = 15.6 in.: crank-pin: length = diam. = 5.4 in.; length of connecting- rod =2.25 X stroke; crank-throws: 6 in. wide X 3.7 in. thick; diam. of wrist-pin = 2.8 in . Gas Turbines. The best results are obtained with high compression, rapid introduction of heat (around 900 B.T.U. per lb.), and by an exhaust temp, of about 1,300° F. absolute. The charge should be compressed to about 570 lbs., maintained at about 140 lbs. in combustion-chamber, and exhausted at or below atmospheric pressure. Velocity at nozzle varies from 1,600 to 2,600 ft. per sec. according as the temp, of combustion ranges from 1,800° to 4,500° F., absolute. For a temp, of 3,600° F. abs. (com- pression 350 lbs.), the sectional area of combustion-chamber = 100 X sec- tional area of nozzle, and vol. = sectional area X 6 to 10 times the diam Nozzles to resist heat are made of corundum, metal-tipped. Peripheral speecl of wheels should not excee<l 660 ft. per sec. Wheels and vanes shotiM l)e made of nickel .steel, which is not weakened or unduly oxidized by the temperatures employed. (L. Sekutowicz, Mem. Soc. des Ingenieurs Civils, France.) 180 APPENDIX. Compressed Air. Blowers and Compressors. Pressures employed Capacities „ , , , lbs. per sq. in. (gauge), (cu. ft. per min.). For blaat-furnaoes, 4 to 10 lbs. Up to 65,000 * * Bessemer converters, 15 " 45 ' * .... 30^000 " compressed-air transmission, 70 " 115 *' " '* 10,000 " ** reservoir storage 1 ,000 and upwards 2,000 (for torpedo boats) For pressures above 75 lbs., two- or three-stage compression should be employed, the air passing from compression cylinders into intercoolers, where it is split up into thin streams and flows over the surfaces of tubes chilled by water circulatin g through them. For two-s tage compression, pressure in intercooler = v^final pressure to be obtained. For three-stage compression (high p ressures, 1,000 lbs. and] over), pre ssure in first i nter- cooler = V final pres.; pressure in second in tercooler = 'v square of final pres. The mean piston velocities employed range from 400 to 6(X) ft. per min. Blowers for blast-furnaces have strokes of from 3 to 6 ft., and r.p.m. up to 50. Air and steam cylinders are generally of equal dimensions and have the same length of stroke, pm (air) =ijpm (steam). For large, horizontal blast-furnace blowers ij = 0.85, for blowers for converters and compressors i? = 0.75 to 0.85 (tj = mechanical efficiency). The volumetric efficiency ranges from 90 to 95%. It may be deter- mined from the low-pressure cyl. diagram: Volumetric efficiency = length of card on atmospheric linen- total length between the extreme end ordi- nates of card. Velocity of flow through valves = 3,000 to 5,000 ft. per min. (suction), =5,(X)0 to 7,000 ft per min. (compression). I. H. P. = 144carQ(p- 14.7)-*- (0.9X33,000), where c = 1.3 to 1.4 for blast- furnace blowers, =1.35 to 1.5 for compressors and blowers for converters; Q = cu. ft. of air per min.; p= absolute pressure of air in lbs. per sq. in.; 0.9 = speciflc weight of air at 29.62 in. of mercury and at 77® F. compared with air at 29.92 in. of mercury and at 32** F. Values of x: Forp« 25 50 76 100 125 a; (poor cooling) = .81 .61 .50 .44 .40 X (efficient cooling, compression ac- cording to piji ^s) = .77 .57 .46 .40 .35 Ft.-lbs. of work theoretically required to compress 1 cu. ft. of free air from p to pi = (3.44 X 144p) [ (— ) - 1 J (see page 1 02) . Rotary Blowers consist of two impeller wheels revolving in a close-fitting casing with equal velocities and in opposite directions, the air being drawn in at right angles to the axes of impellers and delivered compressed at the opposite opening. The profil'^s of the impellers are developed in the same manner as are the teeth of gear-wheels. Capacity in cu. ft. per sec, q'^XNrBiD^- A) -h(4y SO), where JV = r.p.m.; B = axial length, and Z) = diam. of impellers, both in feet; A^^area of cross-section of impeller in sq. ft.; -^=volun)etric efficiency =0.6 to 0.95. Mechanical efficiency ranges from 0.45 to 0.85. Pressures from 12 to 80 in. of water (0.43 to 2.9 lbs. per sq. in.). Mechanical Refrigeration. Plate Ice vs. Can Ice. Plate ice does not require the use of distilled water in its production. 1 lb of coal will make about 10 lbs. of plate ice, some 275 sq. ft. of freezing surface being required per ton capacity. In the manufacture of can ice filtered or distilled water must be used, otherwise the impurities contained in ordinary water will be retained in the oore of the block. Can ice does not keep well when stored. 1 lb. coal will make from 6 to 7^ lbs. of can ice. Plate systems cost from 40 to APPEJNDIX. 181 75% more than can systems. (For 50-ton plant, a can syBtem costs about $550 per ton capacity). Heating and Ventilation, « Heat liOSses due to conduction and radiation, H (in B.T.U.) = Equiva lent glass surface, ^X(/ + 15*'), where indifference between temp, of room and outside temp. = 70° F., generally. „ Exposed wall surface ^. . Exposed ceiling or floor surface 4 20 (Surfaces in sq. ft.) Exposed surfaces are those one side of which is subjected to temp, of outside air. To /f must be added, V — ~l^ to provide for ventilation losses, where n=«No. of changes of air per hour, c = contents of room in cubic ft. The total loss {H-\rV) must be increased 16% for E. exposures and 26% for N. and W. exposures. Hot- Air Heating, Air should be heated to about 140° F. No. of cu. ft. of air heated from 0° to 140° = Q = total heat loss in B.T.U. -4-2.87. Assuming that 6 lbs. of coal are burnt per sq. ft. of grate-area per hr., and that each lb. supplies 8,000 B.T.U., area of grate in sq. ft. = Q-4-14,(X)0. The heating surface of furnace should be from 12 to 20 times the grate area, 1 sq. ft. of heating surface giving off about 2,500 B.T.U. per hr. The fire-pot should not be less than 12 in. deep, and the cold-air box should have an area of about 75% of the combined cross-Pection of all the pipes. For an average outside temp, of 25° F., from 1.75 to 2 lbs, of coal are burnt per hr. per sq. ft. of grate area For temp, of —5° F., from 4 to 4,5 Iba. Area of Pipes for Hot- Air Heating. Volume of air in cu. ft per min. F = .E:«-I-15)-5-(60X1.1). Velocities of air, v = 280, 400, and 500 ft. per min. for 1st, 2d, and 3a floor s respectiv ely. Area of pipes in sq. ft. = V+r^ or, diam. of pipe in in. = vi84F-f-v. Area of air outlets should exceed I. IX grate area. Area of registers = 1.25 X area of pipe supplying same. (Gondfensed from Proceedings Am. Soc. Htg. and Vent. Engrs., W. G. Snow and I. P. Bird.) Blower System of Heating and Ventilating. In this system the air is blown by means of a fan over coils of pipe through which steam cir- culates. Cu. ft. of air required = Total B.T.U. required -^ 55(1 40 -70), where 140 = degs. F. air is to be heated, and 70 = degs. F temp to which rooms are to be heated. The coils are generally of 1-in. pipe, from 200 to 250 linear ft. of pipe being used per 1,000 cu. ft. of air to be heated per min. Air velocities (ft. per min.): Mains, 1,500-2,000; branches to register flues, 1,000-1,200; flues to registers, 500-700; from registers, 300—500 Steam Heating, Sizes of Mains for. (Indirect Radiation.) Sq. ft. of radiating surface supplied by pipe 100 ft. long = A. A = ( 82 + 2.3 p)<P'**, where p<16 lbs. (i lb. allowed for drop). A = (138 + 2.15p)d2". *• p>16 •* (i " " " " For other lengths, multiply by factor c. L in ft. = 50 200 400 600 800 1,000 1.4 .7 .51 .41 .35 .31 (p=abs. pressure in lbs. per sq. in.; <f = diam. of pipe in in.) Diam. of returns, di=0.6d when d>7 in. If d<4 in., dx is one size smaller; if d = 4 to 7 in., di = 3i in. Direct Radiation: For W.I. -pipe radiators, A will be 20% greater than above for a given diam. rf, and for C.I. radiators 30% greater [The foregoing has been digested from matter contained in The En^ gineer (Chicago) for Jan. '06.] Compare with: Square feet of radiating surface = lbs. steam per min. X 145 ( = lbs. steam per min.X60 min.X966 B.T.U. per lb.-s-400 B.T.U. radiated per sq. ft. per hour). See also formulas on page 70 for Flow of Steam in Pipes. 182 APPENDIX. Cooling of Hot- Water Pipes. Ordinary 2-m. pipes (0.154 in. thick) with water at 140° F. cooling to 32° F. (air about 7° F.) lose approxi- mately as follows: 0.55 B.T.U. per sq. ft per hr. per degree drop in temp (still air). 1.05 B.T.U. per sq. ft per hr. per degree drop in temp, (air moving 1 ft. i.rB-~^- 1.6 B.T.U. per sq. ft. per hr per degree drop in temp, (in still water at 32° F.). 4.5 B.T.U. per sq. ft. per hr. per degree drop in temp (in water moving ' i in. per sec). Poujcr, Feb. '06.) HYDRAULICS AND HYDRAULIC MACHINERY, Plttnger-Pumps. Strainer area =(2 to 3) X cross-section of suction- tube. Area of valve-passages = (1 5 to 2) X cross-section of suction-tube. Valves should be of pure rubber. Suction air-chamber vol. = (5 to 10) X vol. of pump cvl. Suction veloc- itv = 150 to 200 ft. per min. Vol of pressure air-chamber = (6 to 8)Xvol. of pump cyl. Pressure velocity = 200 ft. per min. for large pumps and long pipes, = 300 to 400 ft. per min. for small pumps and short pipes. Thickness of cyl. wall = 0.024 -I- 0.4 in. for vertical pumps (for horizontal pumps make thickness 25% greater). Thickness of air-chamber walls, < = 0.42pd-^(/« — p), where p==lb8. per sq in., gauge, ft (safe) = 2,100 for C. I. =8,500 to 10,000 for W I. Efficiencies upto 93%, usually 80 to 85%. Centrifugal Pumps. Outer rim velocity in ft. per sec., V; = 2jrriiV -?- 60; relative discharge velocity, do., =vrf = 0^3 (^3= entering velocity of water). <p=r^-i-ribi sin a. (r,, b^ and rz, 62= outer and inner radii of wheels and vane widths, respectively; a = angle included between tangent to wheel (in direction of motion) and direction of end element of a vf.ne, produced). Theoretical pressure height, Hi = (ih^ -\- vdvj cos a) ■i-g( = 1.3H for short conductors and 1.5H for average lengths). H^ total height of delivery = suction head + pressure head. Head against wnich pump can lift = (vi^—v^^-^2g. rj = 2r2 (diam. of suction-tube is made equal to rO; t>3 = 3 to 10 It. per sec. No of vanes = Z = 6 to 12. Efficiency of best pumps is around 80%. Cu. ft. of water pumped per sec, = (^2ar2 — : /&2^» where ai= angle between tangent to vane at inner end, and tangent to inner circle of radius r2; t= thickness of vane in ft. Pum ping-Engines. Area of valve-seat openings = area of plunger X plunger speed in ft. per min. 4-200. (Chas. A. Hague.) SHOP DATA. High-Speed Steel Practice (Speeds in ft. per min., cuts in in.). Light Heavy Speed. Cut. Speed. Cut. C. I., medium, 75 AXa^ 47 iX C. I. (hard), tool-steel 35 20 X Steel, soft. 150 67 X " hard. 92 50 . X Mall, iron, 100 80 AX Brass, 120 90 iX Chilled iron 3 to 12 ft. per min , all cuts. The above values for turning are for diameters of work>6 in.; for smalleii diams. use speeds 10 to 15% lower. For milling, multiply above speeds by 1.5, — for boring, multiply by 0.6 to 0.8. APPENDIX. 183 Drilling: Average peripheral speeds (feeds 0.008 to 0.02 in. per rev. for drills>i in ): Material, C. I. Steel. Mall. Iron. Tool Steel. Brass. Speeds, 80 67 78 33 127 Reaming: Periph. speed = Periph. speed of drill of same size X 2 -i- No. of lips on reamer. Feed for reamer = | (drill feed X No. of reamer lips). Milling: Periph. speed of cutter for a cut i in. deep, and a feed of 0.01 in. per tooth of cutter per rev.: C. I., 90; mall, iron, 86; soft steel, 76; tool steel, 37; brass, 140. Planing: 50 ft. per min. for steel. (O. M. Becker, Eng. Mag., Aug. '06.) Turning: Steel Shafting. G. I. Forged Steel. Ft per min., 61 150 102 160 32-100 Lbs. per min.. 3.64 2.75 6.6 10 36 Milling: Steel. C. I. Cut, 7i X i in., 6 ft. per min. 6 X i in., 4 ft. per min. Lbs. per min., 6.4 6 Drilling: 50 to 100% higher speeds than given above by Becker. (Results with **A. W." steel; Engineerina, London, 12-16-'05.) Tool. Material. Ft. per min. Lbs. per min. Lathe, G. I., 106 2.63 Steel, 44 2.3 to 3.43 170 1.69 W. I.. 64 4.2 Wheel-lathe, Steel, 14 6. Planer, Gast steel, 30 3.2 G. I.. 29 18.3 Brass. 120 2.03 i (U in.). W. I.. 64 .88 Boring-mill, Steel, 60 1.1 (G. M. Gampbell, Am. Mack,, l-26-*06.) The average cutting force varies from 100,000 lbs. per sq. in. for soft C. I. to 170,000 lbs. for hard G. I. Very hard G. I. may be cut at 25 ft. per min.: above 125 ft. per min. for G. I., tools begin to wear rapidly. (Univ. of ni. tests.) H.F. Required by Machine Tools =-CX lbs. removed per min. C»> 2.6 for hard steel, 2 for W. I., 1.8 for soft steel, and 1.4 for C. I. (G. M. CampbeU, W. Soc. Eng'rs, Feb. '06.) Standards for Machine Screws (Threads U. S. Form., — proposed by Committee of A. S. M. E., May, '06). p" =» pitch = 1 + No. of threads per in.; d =» depth =0.70366i)"; flat at top — p"+8; flat at root of thread — p"-*- 16. i>— diam. of body of screw. Diam. of Thickness of <— Slot-> Head. Head, t. Width. Depth. Round Head. 1.83i> 0.703Z> 0.235i> 0.4Z> Flat Head (countersunk), 2D ^7^7^^ ** OZ^^ Oval Fillister Head, 1.6D '.80D ** 0.4Z> Flat '* " 1.6i) 0.65D ** 0.326D Round Head: Radius of top of head — 1 .096D; radius of sides of head — 0.7D. Oval fillister head: Radius of head-2.186I>, thickness of flat- 0.66D. Included angle of flat head -82°. Diam. in in., 0.07 0.086 0.1 0.11 0.126 0.14 0.165 Threads per in., 72 64 66 48 44 40 36 Diam. inin., 0.19 0.213 0.24 0.25 0.27 0.32 0.376 Threads per in., 32 28 24 24 22 20 16 Force Fits. Pressure required in tons — 786dZ^-»-rf*.°*, where d — diam. of piece. Z— length, d— allowance for fit, all in inches. (S. H. Moore.) 184 APPENDIX. International Metric Threads. Anele of thread » 60^. The top of thread is flatted off (i of its height) and the bottom is rounded to A its height, making total depth of thread =HX the depth of a sharp V thread of same pitch. Cost of Electric Power. — In large street-railway power-houses (2,000 to 10,000 kw. capacity) with coal costing $3.50 per ton, the cost of one kilowatt hour at the switchboard is about $0.0078. (C. H. Hile, Power, Nov. "06.) Miscellaneous Machine Design. Power-Hammers. Lifting force P = weight of hammer TTX a, where « = 1.2 to 2. Lift L = 3 to 6 ft., TF = 100 to 2,000 lbs. Velocity = 150 to 250 ft. per min.; strokes per min. = 20 to 30 Steam-Hammers. TT «= 50,000 to 260,000 lb?., a = 1.5 to 2. No. of strokes per min. = 72 -^v^. Greatest lift L, ,in ft., =0.25''^'^. Diam. of piston-rod in in. = 0.055V^. For small hammers (W = 150 to 2,000 lbs.), a-2 to 3.5. Piston-rod diam. in in. = (0.5 to 0.65) X piston diam. Weight of Anvil and Base Wi^'cLW; (c = 1.8 for iron forging, =3 for Bteel-work) Pressure exerted on anvil =a;LTF + Pri, where a: = 18 to 25 for iron-work, and 25 to 35 for steel. Riveters are designed to furnish 100,000 to 200,000 lbs. pressure per sq. in. of rivet section (according to the hardness of rivets), and about one-third of this pressure for holding plates together while being riveted. Bending Rolls. Diam. of roll <2=2V^, where 6 » width of plate, and t = thickness (d, 6, and t in in.). Punches. Diam. of punch di=d, or d—^t; diam. of hole in die = ^'i+i'; (<i=diam. of hole in plate, t = thickness of plate, both in in.). Greatest force required = o;ra^ o (or shearing strength of material in lbs. per sq. in.) = 84,000 to 100,000 for steel plates, =55,000 to 85,000 for W.I. ( = 17,000 to 28,000 when heated to a dark red), =35,000 to 55,000 for copper, =13,000 to 20,(XX) for zinc. Velocity of stroke — 3 to 4 ft. per min. Shears. Vertical clearance of blades = 2°; angle of cutting edge of blades = 75** (approx). Angle included between cutting edges of both blades = a = 8° to 10*. Greatest pressure required (when a = 0°)=<i6^ where 6 = width of blade and < = thickness of plate to be sheared. Pressure required when a>0° = -7 . Cutting speed =3 to 6 ft. per min. tan « Circular Shears are used for cutting sheets up to 0.2 in. in thickness. Diam. of blades = 70 X thickness of sheets to be cut, circumferential speed = 100 to 200 ft. per min. Rolls for W. I. Diam. of roll in in. d=(fi—f^)-i-il —cos 0), where e is obtained from the relation, tan 6 = m- ft for W.I. at rolling heat is approx. equal to 01, whence d=(/i — <2)X200. (<i= thickness of metal before ruling, f2=' thickness after). Planers. Speed for tables over 6 ft. wide = 12 to 20 ft. per min.; for tables less than 6 ft. wide, from 20 to 28 ft. Return speed = 4 X cutting speed. Shapers. Gutting speeds up to 48 ft. per min.; return speeds = 4 X cut- ting speed. Belt-Conveyors. Rubber-covered belts from 8 to 60 in. wide running on rollers (3 to 5 in. in diam.) are used for convesring grain, coal, ashes, etc., where the angle of elevation is not over 23*. Spacing of Rollers. Driving side. Return side. Grain 6 to 12 ft. 12 to 18 ft Coal 4to 6** 8tol2** For changing direction guide rollers 6 to 8 in. diam. are used; if the deviation is abrupt, rollers from 12 to 20 in. diam. are employed. The tension of belt is maintained by weights or a screw. APPENDIX. 185 Belt Velocities F, in ft. per min.: Bran, light grains, etc., 400; heavy grain, 600 to 600. Coal (horisontal belt), 460; elevating, 660 to 900. Sorting or gathering belts, up to 60. Cubic feet moved per hour -0.0224^(0.06 -2)2, where 6 -width of belt in in. Screw-Conveyors consist of sheet-metal helicoids mounted on hollow shafts, with l:>earings 8 ft. apart for a 4-in. screw (up to 12 ft. apart for an 18-in. screw). Used where elevation angle is less than 30*^. Troughs of sheet metal 0.08 to 0.16 in. thick; clearance between screw and trough— 0.12 to 0.25 in. Spirals of rectangular-section steel bars woimd e^fewise and connected to shaft at about every 20 in. perform about 20% less work than screw conveyors. Sections of spirals. 0.8X0.2 in. 1.5X0.28 2.5X0.28 3X0.28 Ditou. of troui^. 4 in. 8 in. 12 in. 20 in. Diam. of screw d<l7 in., generally. Pitch of spirals— 0.7<l. R.p.m.— 282-s-V5r If 42% of the cross-section of trough is assiuned to be filled with the material to be moved, then, Cu. ft. moved per hr. — 2.265v^. H.P. required -(0;061 to 0.091) XLgr. where i- length of screw in ft., 9— cu. It. delivered per sec, and r^lbs- per cu. ft. of the material moved. EliECTBOTECHNICS. StoTase Batteries consist of lead plates immersed in dilute sulphurie acid. These plates are either coated with a paste made of red lead (or red lead and litharae). or they are cast in the form of grids, the paste being forced into the holes of the grids under pressure. The number of negative plates is always one more than the number of positive plates. The H^Oa must be pure (free from HNO3, HCl, and Sb) and diluted only with distilled water, the acid being always poured into the water, — ^never vice veraa. The dilute acid or electrolsrte should have a sp. g. of about 1.14 ( — 19** Baum^) at the beginning of a charge, which rises to 1.18 to 1 2 (23° to 25** Baum^) at the completion of charge. The density becomes altered in use through evaporation of water, loss through ebullition, etc., and water or add should be added from time to time to keep the plates covered with i to i in. of the electrolyte. The sp. g. is the best guide to the condition of the cell. Voltage t)f cell — 2 volts, approx.,at beginning of charge, rising slowly to 2.2 volts, thence more rapidly to 2.7 volts. Discharge begins at about 2 volts, quickly dropping to 1.97 volts, then slowly to 1.9 volts and then rapidly to 1.83 volts. If no current is taken from cell, its voltage is about 2 volts, regardless of the degree to which it is charged. Current strength varies (aceovding to size and construc- tion of ceU) from 5.5 to 8.4 amperes per sq. ft. of plate area (charging), to 8.4 to 11 amp. per sq. ft. (discharging), or 1.1 to 1.3 amp. per lb. of plates. CaiMtcity is measured by the number of ampere-hours which a cell will yield up to a certain defined drop in voltage (7 to 20%) down to 1.83 volts. The capacity is greater the slower the discharge and varies from 1.8 to 3.6 amp.-hr. per lb. of plates (rapid discharge) to 5.5 to 7 amp.-hr. per lb. (slow discharge). Efficiency: — Good cells yield from 90 to 95% of the amperage with which they are charged, and (the voltage of discharge being lower than that of charge) from 75 to 85% of charging energy in watts. The first charge must be undertaken as soon as the electrolyte is poured into the cells and it should continue until the positive plates have a dark- brown color and the sp. g. of elect. olyte has risen from 1.14 to at least 1.18. Time required: from 16 to 50 hours. Charging is generally accom- plished with voltages up to 2.4 volts for a steady current, and is interrupted when gas bubbles slowly begin to form at about 2.25 volts (i.e , when violent ebullition occurs at about 2.5 volts) C!ells should be fully chaived when lying unused, and should be recharged every 10 days or so, if possible 1S6 APPENDIX. The Dielectric Strength of Insulating; Materials ocV thickness, generally (for Para rubber, strength oc thickness). (Approx. vfdues be- low.) Volts for Volts for Material. 1 mm. Material. 1 mm. thickness. thickness. Ordinary paper 1,500 Varnished paper and linen. 10,500 Fiber and MJEuiila paper. . . . 2,200 Ebonite 28,500 Presspahn and Impregnated Rubber 21,000 paper 4,600 Gutta-percha 19,000 Para rubber 15,500 (C. Einsbrunner, Electrician, London, 9-29 and 10-6-'06.) Electro-niasnetSt Table for Winding. g- Single. Double- s Single- Double- covered, covered. covered, covered, ^QQ Turns Turns goQ Turns Turns •s<« "S^ 'd5 Kf per Sq. In. K' per Sq. In. r K! per Sq.In. S' per Sq. In. 4 4.73 26.1 4.58 24.5 18 22.08 568.7 19.88 461.1 5 5.29 32.7 5.11 30.5 19 25.07 733.3 22.8 606.5 6 5.92 40.9 5.68 37.7 20 27.81 902.2 25.03 730.9 7 6.61 51. 6.32 46.6 21 30.81 1107.6 27.41 876.6 8 7.55 64.2 7.18 60.1 22 34.07 1354.3 29.98 1048.4 9 8.24 79.1 7.81 71.2 23 37.64 1652.8 32.68 1245.8 10 9.18 98.3 8.63 86.9 24 41.49 2008.2 35.59 1477.7 11 10.44 127.2 9.88 113.8 25 45.66 2432.4 38.6 1738.2 12 11.65 158.3 11.01 141.4 26 50.15 2933.8 41.77 2035.5 13 13. 197.1 12.21 173.9 27 54.95 3522.9 45.04 2366.4 14 14.48 244.6 13.5 212.6 28 60.1 4213. 48.45 2738.4 15 16.11 302.9 14.8 255.5 29 65.57 5016.2 51.96 3149.9 16 17.92 374.7 16.44 315.3 30 71.27 5926.1 56.47 3589.5 17 19.9 461.9 18.26 388.9 'Turns per sq. in.'' are calculated on the assumption that the number of layers per in. depth = No. of turns per in. (linear) X 1.166 (or 16}% in- crease per in. due to imbedment of layers), and that "Turns per sq. in."» 1.166 X (turns per in.)*. No. or feet of wire in 1 cu. in., L= Turns per sq. in. + 12. Ohms resistance per cu. in. =L X No. of ohms per linear foot (see table on page 155). Insulation assumed, d (diam. of covered wire'^'diam. of bare wire+^): Size of Wire, Single-covered, ^ = Double-covered, d" 4 to 10 inclusive 0.007 in. 0.014 in. 11 to 18 inclusive 0.006 in. 0.010 in. 19 and up 0.004 in. 0.008 in. E. M. F. of Dynamos. Let 2p = No of poles, 2aBNo. of parallel ar- mature branches into which the current divides; then, ^E? = #0*1057: —10~*. oU a Let a=^-i-T(>l'=pole arc, t= polar pitch), B{= induction in air-gap, Z)«« diam. of armature in cm., Z= length of armature in cm. Then, kilowatt capacity of generator «=cZiVD210-«, where c^aBiA10~^-i-6. (A«=No. of ampere-conductors per cm. of circumference, =no/a-i-2jrZ>, where /«» am- peres in each conductor) A (ordinarily = 200) may reach 300 to 360, with high Bi, strong saturation of teeth and good ventilation. (If a — 6 to 0.85, Bj = 6,000 to 10,000, .4 = 150 to 200, then c= 1 to 3.) The current volume in one slot of an armature (— /«fio) should not exceed 900 amp. APPENDIX. 187 If /«<70 amp., round wire should be used; if >70 amp., conductors of rectangular section are preferable. No. of commutator segments— 0.04noV/a. For no see bottom of page 136. Current density in armature conductors: 2 to 5 amp. per sq. mm. (=400 to 1,000 cir. mils per amp. » 1,300 to 3,200 amp. per sq. in.). Tooth saturation: maximum (at root) — 16,0()0 to 23,000 lines per sq. cm.; minimiun (at periphery) - 14,000 to 20,000. Saturation of core: 7,000 to 12,0(X), — lower value for multipolar machines. For cooling of armature allow 5 to 10 sq. cm. of external surface for each watt wasted. (Kapp.) Brushes: each metal brush should cover from 1 to 2i conmiutator segments (carbon, 2 to 3^). Interpoles, Motors and Generators with, Interpoles are used be- tween the main poles of multipolar machines for the purpose of neutralizing the armature magneto-motive force and the reactance voltage due to the fihort-cireuiting of the armature coils by the brushes, sparking being thereby reduced to a minimum. The higher the speed, the voltage, and the output, the greater are the advantages derived from their use. Koughly, for gen- erators, K.W. Voltage. R.P.M. Interpoles are: 750 and up 250 and up 1,500 and up To be used. 250 250 1,000 Of slight advantage. 100 250 1.000 •• ** 100 and up 250^500 100 " no 400 •• •• 600 200 To be used. fiOO •• •• 250 200 In the second and third cases, interpoles are more satisfactory, but they increase cost of construction, and good designs are available without usin^ them. Interpoles are extensively used in small motors and dynamos t>f high and moderate speeds, but where heating and not sparkii^ is the limit of output, their use is attended with increased cost, lowered efficiency, and no especial advantages. The peripheral speed of commutator should not exceed 115 ft. per sec, and conmiutator should be large enough to radiate the heat generated, 1 sq. in. of surface being allowed for each 60 amperes of current taken off. The leakage or dispersion coefficient is larger than in designs without interpoles, being 1.35 for the main magnetic circuits and 1.45 for tne aux- iliary or interpole circuits. To calculate the flux required to enter the armature from the interpoles, let 1— length of conductor (in cm.) which actually cuts the auxiliary field. Then, i- 1.1X0.7X6, where 6=breadth of pole-shoe (l| to shaft), 1.1- coefficient to allow for "fringing" or spreading of field at the pole-tips, and 0.7 — that portion of the length of conductor which is active (i.e., im- bedded in the armature iron, the remaining 0.3 being taken up by air^ ducts, insulation, etc.). Let 5— peripheral speed of armature in cm. per sec^and £ — average density in the air-gap of interpole in lines per sq. cm. Then, E.M.F. gen- erated by one conductor— BiS'lO'^. As there are two conductors in the short-circuited turn, E.M.F. in one turn — 2BiLS * 10"^^ and this must suffice to neutralise the reactance voltage. If v— mean reactance voltage [ — re- actance voltage + (jr-5-2)], » — 2B>LSfl0-*, whence B, or the desired flux dematy-v' 1^+2X8. See pages 140-143. (H. M. Hobart, Elec. Review, N. Y., l-20-'06.) Resistance of Iron and Steel Bails. Iron rails have x times the resistance of copper conductors of same cross-section and the content of manganese in the iron seems to be the chief factor in increasing the value of X. For continuous currents, x — 5 + 7 Mn (roughly), where Mn — per cent of manganese. A very good rail used in London and contaimng 0.19% Mn has a measured value of s-6.4. (By formula: s-5+ (7 X0.19) INDEX. Absolute temperature, 58 Acceleration, 43, 71 Adiabatics, 61 Admittance, 148 Air, 100-103 -chambers, 114 compressed, 101, 180 flow of, 101, 161 -mp, 141 -lift pump, 114 -passages, 90 -pumps, 94, 174, 176 -space, 141 Alcohol, denatured, 177 Algebra, 1 iUloys, 11, 162 Alternating currents, 145 generators for, 148 Altitudes, 101 Aluminum. 11, 163 wires, 156 Ammonia, 103 Ampere, 130 -turns, calculation of, 138 Angle of torsion, 22 Angles, pipe, 109 steel, Carnegie, 34-35 Annealing, 118 Anode, 131 Arc lamps, 159 Areas of circles, 2 of plane figures, 5, 162 Arithmetic, 1 Arithmetical progression, 4 Armature, 136 shafts. 139 Artificial draft, 93 Atomic weights, 10 Babbitt metal, 11 Balancing, 85 Ball beanngs, 47, 169 Barometric condmiser, 175 Batteries, storage, 185 Beams, deflection of, 26 I-, Carnegie steel, 32 of uniform strength, 29 Bearings, journal, 46, 168 Belt-conveyors, 128, 184 Belting, 51 Bending moment, 23 and compression, 30 and tension, 29 and torsion, 31, 166 stress, 23 Bends, pipe, 109 Bevel ^ears, 50, 170 Binomial theorem, 3 Blacksmith shop, the, 117 Block and tackle, 45, 171 Blowers, 102, 180 ' Boiler accessory apparatus, 93 dimensions, 88 efficiencies, 87 shell plates, 87 test, 115 tubes, 14, 87 Boilers, steam, 87 performance of, 87 proportions, 89 Bolts, flange-coupling, 22 dimensions of heads, 120 strength of, 21-22 weight of, 15 Braces and stays, 88 Brake, Prony, 55 Brakes, band and friction, 171 Brass, 11 Brasses, journal, 47 Breaking stresses, 19-20 Brick masonry, 17 Bridge trusses, 40 British thermal unit, 57 Bronzes, 11-12 Brushes, dynamo, 139 Building Materials: breaking stresses of, 19 weights of, 12 Calorie, 57 Calorific values of fuels, 91 of gases, 96-97 Capacities of oonduetors, 159 Capacity, 130, 147 Carborundum, 122 Carnegie structural steel, tables, 31-36 Carrying capacity of conductors, 159 Case-hardening, 118 189 190 INDEX. GastinffBt shrinkage of, 117 weight of, 117 Cast-iron columns, 31 pipe, 13 properties of, 11 Cathode, 131 Cement, 12, 36, 163 Center of gravity, graphically, 24 position of, 25. 162 Center of oscillation, 43 of pressure, 106 Centigrade thermometer, 57 Centrifugal fans. 102 force, 21 force in fly-wheels, 73 pumps, 113, 182 Chains, crane, 16 strength of, 20 Channel, steel, 33 Chemical data, 10 Chimney draft, 92 ^ases, 92 Chmmeys, steel, 167 Chords of circles. 5 Circles, areas ana circumferences of, 2-3, 5 Circuits, calculation of, 157 Circular pitch, 49 Circulating-pumps, 94. 175 Circumferences of circles, 2-3 Clearance in cylinders, 63, 75, 97 Coal, analyses of, 91 consumption, 85 -gas, 81 Codes, 109 Coefficients of friction, 53 Collapse, 31, 166 Colhir bearings, 47, 54 Columns and struts, 30, 165 Combined stresses, 29-31 Combustion, 90, 175 rate of, 93 Conmiutator, 139 Composition of substances, 10 Compound interest, 3 Compressed-air, 101, 180 Compression and bending, 30 and torsion, 31 Compression, steam, 63 -gas engine, 97 Compressive stress, 21 Compressors, air, 180 Concrete, reinforced, 36 Condensation, initial, 62 Condensers, 59, 93 electrical, 147-148 Conductance, 131 Conduction of heat, 56 Conductors, electrical, 154 resistance of, 131 Cone, 8 Cone pulleys, 52 Conic frustum, 8 Conical springs, 23 Connecting-rod ends, 46, 168 Connecting-rods, 45, 74, 168, 174 Continuous beams, 26 Convection of heat. 57 • Conveyors, belt. 128, 184 Cooling-water, lor condensers, 50 for gas-engines, 97. 161 Copper, properties ot, 11 Copper wire, tables, 154-155 Corliss valves, 70. 172 Corrosion, 95, 176 Corrugated iron, wt. of, 13 Cotter-joints, 22" Cotton-covered wires, 137 transmission rope, 53 Coulomb, 130 Coupling bolts, flange-, 22 Couplings, 169 . Crane chains, 16 hooks, 29 Cranes, electric, 128 hydraulic, 116 Crank-arms, 46 -effort diagrams, 71 pins, 47, 75 shafts, 46. 75, 166, 174 throws, 100, 174 Cube root, 3 Cubes of numbers, 2-3 Cupola, 117 Ciurents, electrical, 130 Cutting speeds of tools, 118-123 Cycloid, 6 Cylinder, 8 Cylinders, gas-engine, 99, 178 hydraulic, 116 steam, 66, 174 Dash-pots, 172 Dead-center, to place engine on, 71 Deflection of beams, 26 allowable, 29 Demagnetization, 141 D^iatured alcohol, 177 Density of saturated steam, 59 Diagram factor, 64 Diagram Zeuner's valve, 68 Diameters of engine cylmders, 66 Diametral pitch, 49 Dies, 118 Diesel en^ne. 82. 99 Differential pulley, 45 Pirection of currents and lines of force, 133 Dispersion, coefficient of, 141 Distillates, calorific values of, 92 Distribution constant, 150 Divided circuits, 131 Draft, chimney, 92 intensity of, 92 pressures, 92 -tubes, 112 Drills, twist; 119 Driving chain, 51, 170 Duty of pumping engines, 114 Djrnamometer, 55 Djrnamoe, continuous-current, 136, 186 design of multipolar, 140 INDBX. 191 Dynamost efficiencies of. 136 Dyne, 132 Eccentric loading of columns, 30 Eccentrics, 46 . «„ Economical steam-engmee, 67 Economisers, 93 Eddy currents, 137-140 Efficiency, boiler, 87 of dynamos, 136 of gas-engines, 07 thermal, 61 Elasticity, 18, l63 moduli of, 18 Elbows, 109 . Electric circuits, calculations, 157 cranes, 128 currents, 130 energy, 130- lighting, 159 locomotive, 161 power, 130 railroading, 160 traction, 160 welding, 117 Electrical units, 130 Electrolysis, 131 Electro-magnetism, 132 Electro-magnets, 134, (table) 186 Electro-motive force, 130, 186 Elements of machines, 44 Elevators, 128 Ellipse, 5 Ellipsoid. 8 Emery wheels, 122 Energy, 44 Engine proportions, gas-, 99, 178 steam-, 74 Engine tests, steam-, 115 Engines, steam consumption of, 67 Entropy, 76 Epicydoidal teeth, 49 Evaporation, "from and at' 212°, 59 heat of, 59 Evaporative condensers, 93 Expansion, 57 coefficients of linear, 18 of gases, 57 Eye-bars, 21 Factors of safety, 19 Fahrenheit thermometer, 57 Farad 130 Faults in indicator cards, 64 Feeder currents, safe, 160 Feed-water heating, 93, 175 Field coils, calculation of, 142 magnets, 138 Fire-box plates, 87 Fits, running, force, shrink, etc., 125, 183 Flagging, 13 Flange-coupling bolts, 22 Flat phites, strength of, 29 Floors, loads on. 16 weight of, 16 Flow of air, 101, 161 of steam, 70 of steam in pipes, 70 of steam through nofesles 83 of water in open channels, 109 of water over weirs, 108 of water through orifices, 107 of water through pipes, 109 Flues, 90 Flux, magnetic, 132 Fly-wheels, 21, 73. 75, 100, 164 Force, 43 Forgings, allowance in machining, 118 Form factor, 150 Foundations for engines, 100 Foundry data, 117 Framed structures, 39 Frequency, 145 Friction, 53 coefficients of. 53 couplings, 169 -gearing, 52 of cup leathers. 116 of iournals, 54 in ball bearings, 48 in water pipes, 108 locomotive, 85 i Fuels, 91, 92, 97 Furnaces, 90 Fuses, 159 Fusible plugs, 94 Fusing points, 11, 12 Galvanized-iron wire, 16 -steel wire, 16 Gap machine frames, 167 Gas, coal-, London, 81 -engine data, 80, 161 -engine design, 99, 178 fue&, 92, 175 -pipe, 13 Gas producers, 176 Gas turbines, 179 Gases, weights of. 10 Gauss, 132 Gay-Lussac's law, 58 Gearing, 48 train of, 45 Gears, proportions of, 51 Geometrical progression, 4 Gilbert, 132 Glass, 12, 13 Gordon's formulas, 30 Governors, 68 Graphite, 55 Grate area, 85 Gravity, center of, 24r-25 force of, 43 Grinding wheels, 122 Grindstones, 122 "Grooving, 95 Gun-metal 11 Gyration, radius of 24 Hammers, 184 I HardnQss of materials, 19 1^ INDEX. Haulage rope»' 16 HCMMI. 107 Heat, 56 latent, 58 sensible, 59 total, 50 -units, 57 Heating of oonductors, 159 and ventilation, 104, 181 surface, 85-87 Helical springs, 22, 164 Henry. 147 High-speed tool steel, 122, 182 twist-drills, 125 Hoisting-engines, 128 speeds, ^16 Horse-power, calculation of, 64, 97, 173 of boilers, 87; metric, 162 of locomotives, 84 Hot-aii( heating, 181 Hydraulic cylinders, 116 crane, 116 gradient, 109 pipe, riveted, 13 power transmission, 116 ram, 114 Hydraulics, 106 Hydrostatic pressure, 106 Hjrperbola, 8 Hyperbolic logarithms, 66 Hysteresis, 133, 140 I-beams, steel, tables of, 32 Illumination, 160 Impact. 43 Impedance, 146, 148 Incandescent lamps, 160 Inclined plane, 45 Incrustation. 95, 176 Indicated horse-power, 64 Indicator diagrams, 63-65 Inductance. 146. 158 Inertia diagrams, 71 moment of, 23-24 Initial condensation. 62-63 Injectors, 94 Insulation, armature, 137 dielectric strength of, 186 resistance, 159 Intensity of draft. 92 of magnetic field, 132 Interest, compound, 3 Internal -combustion ongines, 95, 176 entrooy diagrams for, 79 Interpolation, 4 Interpoles, 187 Involute teeth, 49 Iron, cast- and wrought-, 11 wire, 15 Isothermals, 61 Jackets, steam, 62, 63 Jet condensers, 93 Joule. 130 Joule's law, 131 Journals, 46, 168 friction of, 54 Keys, strength of, 22 Kinetic energy, 44 of steam, 83 Kirchoff's Laws, 131 Lacing, 52 Lag-screws, 15 Laminated springs, 29, 165 Lap, steam, 68 Latent heat, 58 Lead of valves, 68 Lead pipe, 14 Leakage factor (magnetism), 141 steam-, 63-64 Leather belts, 51 Lever, 44 Lifting power of magnets, 134 Lines of force, 132 Loam, 117 Locomotives, electric, 161 steam, 84, 175 Logarithms, common, 4; table, 6 hyperbolic, 66 Lubrication, 54 Machine design, proportioning a se- ries of machines, 1^ miscellaneous, 184 Hscrews, 119, 183 shop, the, 118 Machinery, power required for, 126 Machines, elements of, 44 M^^etic circuit, 133 densities in transformers, 153 field, intensity of, 132 flux, 132 induction, 132 Magnetising force, intensity of, 132 Magneto-motive force, 132 Magnets, electro-, 134 field-, 138 Malleable iron, 163 Manila rope, 53 Marine engines, 173 Marriotte's law, 57 Masonry, brick, 17 Mass, 43 Materials, 11 boiler, 11 hardness of, relative, 19 strength of, 18 Mathematics, 1 Maxwell, 134 Mean spherical candle-power, 160 Measures, English and metric, 1, 10 Mechanical refrigeration, 102 stoking, 93, 176 Mensuration, 5 Metal-cutting saws, 125 Metals, 11. 162 Metric screw-threads, 119, 184 weights and measures, 1, 162 Milling cutters, 118 Moduli of elasticity, 18 INDEX. 193 jxLoduIus section, 23 of rupture, 31 Moisture in steam, 58 Moment of inertia, 23, 24, 26, 165 of resistance, 23 Momentum, 43 Monocyclic generator, 150 Morse tapers, 119 Motors, continuous-current, 143 for machine-tooli, 127 Multiple-expansion diagrams, 66 Multipolar dynamos, design of, 140 Nails, holding power of, 16 wire, 16 Nemst lamp, 160 Neutral axis, 23 Noiiles, flow of steam through, 83 Nuts, number in 100 lbs,, 15 proportions of, 120 Oersted, 132 Ohm, 130 Ohm^s law, 131 Overshot wheels. 111 Paint and painting, 129 Parabola, 5 Paraboloid, 8 Pedestals, 168 Pelton wheel, 111 Pendulum, 43 Performance of boilers, 87 of pumping plant, 115 Periodicity, 145 Permeability, 132 Petroleum, calorific value of, 92 Phase, 145 Pins, 22 Pipe, cast-iron, weight of, 13 strength of, 20 threads on wrought-iron, 14 Pipes, steam, 94 Piston rings, 168, 178 -rods, 74, 168, 174 speeds, 70, 97, 173 -valves, 85 Pistons, 74, 100, 174, 178 Pivots, 47, 54 Planers, 184 Plates, boiler-shell, 87 flat, 29 Plunger electro-magnets, 134 pumps, 114. 182 Pneumatic tools, 102 Poisson's ratio, 18 Polar moment of inertia, 24 Potential energy, 44 Power, 44 coat of, 127, 184 -factor, 146, 157 for shafting, 127 hammers, 44, 184 measurement of, 55 plants, cost of, 127 Power required by catting tools, 125 " machinery, 126, 183 transmission, hydraulic, 116 electric, 157 Priming, 95 Producers, gas, 176 Prony brake, 55 Pulley blocks, 171 Pulleys, 45, 52. 170 cone, 52 Pulsometer, 114 Pumping engines, 114, 182 Pumps, air, 94 centrifuf^, 113, 182 circulating, 94 plunger, 114, 182 Punches and dies, 118, 184 Pyramid, 8; frustum of, 8 Pyrometers, 57 Quantity of electricity, 130 Quarter-phase generator, 149 Badiation of heat, 56, 105 Radius of gyration, 24 Rails, elevation of, 175 resistance of, 160, 187 Ram, hydraulic, 114 Rate of combustion, 93 Ratio of expansion, 63, 66 Rawhide gears, 50 Reactance, 146 voltage, 143 Receiver volume, 75 RecoU, 44 Re-evaporation, 63 Refrigeration, mechanical, 102, 180 Reheating of air, 102 Reinforced concrete, 36, 166 Reluctance, 132 Reluctivity^ 133 Renold chain gear, 51 Resilienee, 18 Resistance, 130 of conductors, 131, 155 of rails, 160, 187 specific, 131 train, 84, 160 Resonance, 148 Rheostats, 144 Rings, strength of, 165 Riveted hydraulic pipe, 13 joints, 21, 161, 164 Riveting, 22 Rivets, boiler, 88, 161 bridge, weight of, 15 proportions of, 21 Roller bearings, 47, 54, 169 Rolls. 184 Roof loads, 17 trusses, 41 Roofing materials, 13 slate, 13 Rope, haulafl^e, 16 manila, 53 strength of, 20 transmission, 16, 53 194 INDEX. Rope, wire hoisting-, 16 Rubber belts, 51 Rupture, modulus of, 31 Safety, factor of, 19, 22 -valve, 45, 94 Sand, 117 Saturated steam, 5S-60, 172 Saws, metal-cutting circular, 125 Scale, 95 Screw, 45 oonves^rs, 185 -propeller, 173 -threads, 119-120, 184 Screws, power transmission, 168 machme, 119 Section modulus, 23 Sector of circle, 5 Segment of circle, 5 of sphere, 8 Self-induction, 137, 146 Sensible heat, 59 Serve tubes, 86 Shaft-<K>uplmgs, 47 Shafting, 46 power absorbed by, 127 Shafts, armature, 139 stiffness of. 22 strength of, 22 Shapers, 184 Shear 1^, 42 stress, 21-28 Shears, 184 Sheet-metal gauges, 121 Shingles, pine, 13 Shop data, 117 Shrink fits, 125 Shrinkage of castings, 117 Simpsoirs rule, 6 Single-phase generator, 148 Sinking fund, 4 Siphon condenser, 175 Skylight and floor glass, 13 SUte, 12, 13 Solenoid, 136 Space factor, 142 Sparking, 137 Specific gravities of substances, 11,12 heat, 57, 104 heats of a gas, 60 inductive capacity, 147 resistance, 131 volume of steam, 61 Spikes, 15 Spiral gears, 50, 170 springs, 23 Splines, 22 Springs, laminated, 29 strength of, 23 Spur gears, 49 Square root, 3 Squares of numbers, 2 Stay-bolts, 88 Stayed surfaces, 29 Steam boilers, 87, 89 consumption by engines, 67, 172 -engine proportionls, 74, 174 Steam>flow, 70, 83 hammers, 184 -heating, 105, 181 jackets, 62, 63 moisture in, 58 -pipe coverings, 56 pipes, 75, 94, 105 ports, 75 saturated, 58-60 superheated, 58, 61-62, 67 turbines, 82 Steel, properties of, 11, 162 Carnegie structural, 31-36 Steels, alloy, properties of, 11 Stiffness of shafts. 22 Stones, weights of various, 12 Storage batteries, 185 Strain, 18 Stray-field, 138 Strength of bolts, 21 of diain, 20 of cotter-joints, 22, 164 of crane-hooks, 29 of cylinders, 20, 164 of eye-bars, 21 of flange-coupling bolts, 22 of flat plates, 29 of gear teeth, 50 of helical springs, 22 of laminated springs, 29 of materials, 18, 163 of pipes, 20 of riveted joints, 21 of ropes, 20 of shafts, 22 of stayed surfaces, 29 Stress, 18 bending, 23 compressive, 21 diagrams for framed structures, 39 due to impulsive load, 18 heat-, 18 shear, 21-28 tensile, 20 torsional, 22 Stresses, breaking, 20 allowable, 163 combined, 29 Structural steel, 31-36 Stuffing boxes, 168 Superheated steam, 58, 61, 62, 67« 172 Superheater surface, 62 Surface-condensers, 93, 174 Surfaces of solids, 7 Susceptibility, 132 T-shapes, Carnegie steel, 34 Tantalum lamp, 160 Tap drills, 119-120 Tapers, Morse, 119 turning, 119 Temper, 11 Temperature, 57 -entropy diagrams, 76 Tempering, 118 Tensile stress, 20 INDEX. 195 Tenflion and bending, 29 Thermal efficiency, 61 Thermometera, 57 Threads, pipe (wrought-iron), 14 screw-, 119-120 Three-phase generator, 150 Thrust bearings, 46, 168 Tin, 11 Tin plate, 13 Tool steel, high-speed, 122» 182 Tooth density (magnetic), 140 Torque, 144 Torsion, an^le of, 22 and bending, 166 and compression, 31 Torsional stress, 22 Total heat. 59 Traction of electro-magnets, 134 Tractive force, 160 power, 84 Train resistance, 84, 160 Transformers, 151 design of, 151 Transmission circuits (electric), 157 rope, 16 Trapezoid, 5 Trigonometry, with table, 8, 9 Trusses. 40 Tubes, boiler, 14, 88 holding power of. 87 Turbines, gas, 179 hydraulic. 111 steam, 82 Twist-drills, 119 hi^-speed, 125 Undershot wheels, 110 Vacuum, 64 Valve-stems, 46 Valves, engine, 68 gate-, 109 Sroportions of, 70, 178 ocity, 43 Ventilation. 104 Volt. 130 Volumes of solids, 7 Water, 106 consumption, 64 pipe, 13 wheels, 110 Watt, 130 Wedge, 45 Weigbt of bolts, 15 of bars. 12 of building materials, 12, 13 of flat wrought-iron bars, 13 of gases, 10 of plates, 12 of rivets, 15 of rods, 12 of round wrought-iron bars, 12 of sheet-metals, 13 of spheres, 12 of square wrought-iron bars, 12 of tubes, 12 of woods, 12 Weights and measures 1 Welding, 117 Wheel and axle. 45 Winding table for magnets 186 Wire, galvaniaed-iron, 16 galvaniaed-steel strand, 16 gauges, 121 oisting rope, 16 iron, 15 nails, 15 rope, 16, 53 steel. 15 Wiring formulas, 156 Wood, calorific value of, 92 Woods, weight of, 12 Work, 18 Worm gearing, 50, 170 Wrought-iron pipe, 14 properties of, 11 Z-bars, Carnegie steel, 35 Zeuner's diagram, 68 Zinc, 11 ^ 1 A pocket-book Df mectianlcDl engln«e CatKJt Science QO6513260